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Talk:Reflexive space

Untitled
additional reflexive space: dim<infinity

non-reflexive spaces: c0, l1,  l_/infty ??

How can Reflixive space be defined as "Banach space", when below one can read "Montel spaces are reflexive." No infinite dimensional Montel space is a Banach space. —Preceding unsigned comment added by 83.23.122.42 (talk) 12:44, 22 March 2009 (UTC)
 * The 'Montel spaces are reflexive' statement is using the definition of reflexive for locally convex TVSs, while the lead only mentions the more restrictive case of reflexivity of normed spaces. Do you think this needs to be clarified? Algebraist 19:37, 22 March 2009 (UTC)
 * I agree with your change to the lede; for the definitions, I believe that the normed case is by far the most important (the only that was mentioned for a long time) so I feel that the normed case definition should be given before, although it is a special case of the TVS definition. --Bdmy (talk) 20:27, 22 March 2009 (UTC)

I am a bit dubious about the name "Kakutani Theorem". I have never heard of it, I cannot find any reference to it, and the mentioned result in Conway's book does not mention the name Kakutani. I suggest that the name be associated with a reference or dropped. Delio.mugnolo (talk) 23:02, 4 December 2011 (UTC)

July 2013
If there are no objections, I'll separate the material devoted to the Banach (reflexive) spaces from the one about (reflexive) locally convex spaces, because what is written (in literature) about reflexive Banach spaces is disproportionally large (with respect to the rest), so that I believe that majority of readers prefer to get information about Banach spaces without going into the general locally convex situation. Besides this I want to create a separate article about super-reflexive Banach spaces and to remove there the material about them. Eozhik (talk) 09:45, 24 July 2013 (UTC)

A question to the authors: the notation $$J:X\to X''$$, where is it from? Is there a standard notation for this map? Eozhik (talk) 17:10, 24 July 2013 (UTC)

I can't force myself to make corrections that I want to make, because I suspect that I will damage the philosophical idea that the authors had in mind when writing this. Please, let me know would you mind if I define reflexive Banach space without references to the article about dual (topological vector) space, but instead on the base of the notion of dual normed space and dual norm? I've just made correction in the article on this topic. My idea is that it is easier to define reflexive Banach space without topology. We must use this possibility, because in my opinion, if something can be explained in a more simple way, the one who explains must use this way. What do you think about this? Eozhik (talk) 20:01, 24 July 2013 (UTC)

 * I am not sure that I understand what you mean by:
 * "I define reflexive Banach space without references to the article about dual (topological vector) space, but instead on the base of the notion of dual normed space and dual norm"
 * Is'nt it the way it was done already, by saying that the map J is onto? (by the way, I don't know where this notation comes from; Megginson uses Q, which I don't consider to be more standard than J) Bdmy (talk) 20:39, 24 July 2013 (UTC)

@Bdmy: Yes, but with one difference. I want to do the following:
 * Suppose $$X$$ is a normed vector space over a number field $$\mathbb F$$ ($$\mathbb F=$$$\mathbb R$ or $$\mathbb F=$$$\mathbb C$) with a norm $$\|\cdot\|$$. Consisder its dual normed space $$X'$$, i.e. the space of all continuous linear functionals from $$X$$ into the base field $${\mathbb F}$$ ($$X'$$ is equipped with the dual norm $$\|\cdot\|'$$):

f\in X'\quad\Longleftrightarrow\quad f:X\to {\mathbb F} $$
 * ($$f$$ is a continuous linear functional).

 * This is a normed space (a Banach space to be precise), and we can consider its dual normed space $$X=(X')'$$, i.e. the space of all continuous linear functionals from $$X'$$ into the base field $${\mathbb F}$$ ($$X$$ is equipped with the norm $$\|\cdot\|''$$ dual to $$\|\cdot\|'$$):

h\in X''\quad\Longleftrightarrow\quad h:X'\to {\mathbb F} $$
 * ($$h$$ is a continuous linear functional).

 * Each vector $$x\in X$$ generates a map $$J(x):X'\to{\mathbb F}$$ by the following formula

J(x)(f)=f(x),\qquad f\in X'. $$
 * It is easy to see that this is a continuoius linear functional on $$X'$$, i.e. $$J(x)\in X''$$. We obtain a map

J:X\to X''. $$
 * Again it is easy to see that this map is linear. From the Hahn-Banach theorem it follows that $$J$$ is always injective and preserves norms:

\forall x\in X\qquad \|J(x)\|''=\|x\|. $$
 * (i.e. $$J$$ maps $$X$$ isometrically onto its image $$J(X)$$ in $$X''$$). But $$J$$ may be not surjective.

 * If the map $$J:X\to X$$ is surjective, then the normed space $$X$$ is called reflexive. This implies that $$X$$ is a Banach space (since $$X$$ is isometric to the Banach space $$X$$).

The difference with what is written now is that in what I suggest there is no reference to the notion of dual topological vector space. In my opinion, this reference complicates the understanding of the question in Banach situation. To understand the idea here the reader must not know what topological vector spaces are, how one can define topology on the dual space, etc. So what I suggest makes the material easier. And this allows to separate the Banach situation from the locally convex one. (Of course, for the locally convex spaces one needs mentioning topologies on dual spaces). What do you think? Eozhik (talk) 05:53, 25 July 2013 (UTC)

 * I have no objection to this, I had the feeling that it was precisely done that way, I never took seriously the link to dual topological vector space.  I think that what you say is the "normal" treatment, as appears in Banach space books, and also for example in the WP article Banach space. Bdmy (talk) 07:43, 25 July 2013 (UTC)

 * OK. In this case, I'll make these corrections. What I described will be the main, conceptual changes, but I think there will be some others, less essential, so I hope you will look and share your opinion. One technical question: is there a canonical notation for this map, $$J:X\to X''$$? Would you mind if I change it? Eozhik (talk) 08:13, 25 July 2013 (UTC)

Bdmy, I now think that maybe you were right when telling that there is no need of removing the material about super-reflexive spaces to a new article, but just in case, what were your reasons? Eozhik (talk) 06:22, 25 July 2013 (UTC)

 * Well, I have no objection to move the most technical content of the section "super-reflexive spaces" to a new article, especially if that section is going to grow more. I just wanted to say that I would like to keep a short summary of the "super-reflexive" notion in the "Reflexive space" article, in case the creation of a separate article is done, with a link to  as usual in WP. Bdmy (talk) 07:43, 25 July 2013 (UTC)
 * Also, Dear Eozhik, please take into account my request that you fill some "edit summaries" for your edits! These summaries are helpful for the people who have the article on their "Watchlist" and who help prevent WP from being damaged by vandals or bad editors. Bdmy (talk) 07:43, 25 July 2013 (UTC)

 * "...fill some "edit summaries" for your edits" -- excuse me, that was my fault. This is because I rarely come to WP. Yes, I also foresee that the material about super-reflexive spaces will grow, so maybe this will be inevitable to create a new article and to move there the main material (of course with keeping a summary here and with links). Maybe you should think about doing this yourself, since you are the author? To tell the truth, I would hesitate to do this, since I am not a specialist in this field. Eozhik (talk) 08:09, 25 July 2013 (UTC)

 * We'll see for a creation. So far I was too lazy for this!  I'll be away for a few hours, hope something remains of this "Reflexive space" article when I'll be back!!! About the notation J, I don't care so much, but you'll have to have the support of a good book to choose a different one, otherwise there is no reason to change.  I agree that Kolmogorov and Fomin is a good book, but too much of it will make this look as being ru.wikipedia!!! (just joking...) Bdmy (talk) 08:59, 25 July 2013 (UTC)

 * I guarantee that something will remain... But you should be prepared for the worse... :) Eozhik (talk) 09:06, 25 July 2013 (UTC)
 * Bdmy, I think, it's enough for today. Eozhik (talk) 12:08, 25 July 2013 (UTC)

homeomorphism?
"isomorphism of topological vector spaces" - a homeomorphism ? — Preceding unsigned comment added by Paulsacc (talk • contribs) 12:26, 25 June 2018 (UTC)

 * Paulsacc, yes, I specified this in footnotes. Eozhik (talk) 06:24, 15 March 2019 (UTC)

title: Talk:Reflexive space


text: User talk:63.198.220.138

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:63.198.220.138


text:
Wartburg Theological Seminary

Wartburg Theological Seminary is a seminary of the Evangelical Lutheran Church in America in Dubuque, Iowa. It offers three graduate-level degrees (MA, MA Diaconal Ministry, and M.Div.), a Theological Education for Emerging Ministries certificate, and a diploma in Anglican Studies, all of which are accredited by the Association of Theological Schools in the United States and Canada and the Higher Learning Commission. Students can also choose to add two concentrations: Youth, Culture, and Mission; and Hispanic Ministry. All three of Wartburg Theological Seminary's master's degrees offer the option for Distributed Learning Programs, which combine online learning, intensive courses on-campus, and residential formation. Wartburg also offers a Fully Distributed Master of Arts option without a semester-long residency requirement.

Three academic and missional centers are found at Wartburg Theological Seminary, built on their historic strengths: the Center for Global Theologies, the Center for Theology & Land (rural ministry), and the Center for Youth Ministries.

The Lutheran Seminary Program in the Southwest is a program of Wartburg Theological Seminary and the Lutheran School of Theology at Chicago. The program educates women and men for ordained ministry through the Theological Education for Emerging Ministry. Wartburg Theological Seminary also has long-term ties with global partners, including: Haiti, Tanzania, Guyana, Namibia, Papua New Guinea (with the PNG Museum located on campus), and others.

Theological orientation
Theological education at Wartburg Theological Seminary is shaped by faithful study and interpretation of the Scripture as God's Word and is informed by Christian tradition and the Lutheran Confessions. Courses are reviewed by students and faculty to ensure they instill the twelve core pastoral diaconal practices outlined on the website. Wartburg is a Reconciling in Christ seminary.

title: Wartburg Theological Seminary


text:
Ormulum

The Ormulum or Orrmulum is a twelfth-century work of biblical exegesis, written by an Augustinian canon named Orrm (or Orrmin) and consisting of just under 19,000 lines of early Middle English verse. Because of the unique phonemic orthography adopted by its author, the work preserves many details of English pronunciation existing at a time when the language was in flux after the Norman conquest of England. Consequently, it is invaluable to philologists and historical linguists in tracing the development of the language.

After a preface and dedication, the work consists of homilies explicating the biblical texts set for the mass throughout the liturgical year. It was intended to be consulted as the texts changed, and is agreed to be tedious and repetitive when read straight through. Only about a fifth of the promised material is in the single manuscript of the work to survive, which is in the Bodleian Library in Oxford.

Orrm developed an idiosyncratic spelling system. Modern scholars have noted that the system reflected his concern with priests' ability to speak the vernacular and may have helped to guide his readers in the pronunciation of the vowels. Many local priests may have been regular speakers of Anglo-Norman French rather than English. Orrm used a strict poetic metre to ensure that readers know which syllables are to be stressed. Modern scholars use these two features to reconstruct Middle English as Orrm spoke it.

Origins
Unusually for work of the period, the Ormulum is neither anonymous nor untitled. Orrm names himself at the end of the dedication:

At the start of the preface, the author identifies himself again, using a different spelling of his name, and gives the work a title:

The name Orrm derives from Old Norse, meaning worm, serpent or dragon. With the suffix of "myn" for "man" (hence "Orrmin"), it was a common name throughout the Danelaw area of England. The metre probably dictated the choice between each of the two forms of the name. The title of the poem, Ormulum, is modeled after the Latin word speculum ("mirror"), so popular in the title of medieval Latin non-fiction works that the term speculum literature is used for the genre.

The Danish name is not unexpected; the language of the Ormulum, an East Midlands dialect, is stringently of the Danelaw. It includes numerous Old Norse phrases (particularly doublets, where an English and Old Norse term are co-joined), but there are very few Old French influences on Orrm's language. Another—likely previous—East Midlands work, the Peterborough Chronicle, shows a great deal of French influence. The linguistic contrast between it and the work of Orrm demonstrates both the sluggishness of the Norman influence in the formerly Danish areas of England and the assimilation of Old Norse features into early Middle English.

According to the work's dedication, Orrm wrote it at the behest of Brother Walter, who was his brother both affterr þe flæshess kinde (biologically, "after the flesh's kind") and as a fellow canon of an Augustinian order. With this information, and the evidence of the dialect of the text, it is possible to propose a place of origin with reasonable certainty. While some scholars, among them Henry Bradley, have regarded the likely origin as Elsham Priory in north Lincolnshire, as of the mid-1990s it became widely accepted that Orrm wrote in the Bourne Abbey in Bourne, Lincolnshire. Two additional pieces of evidence support this conjecture: firstly, Arrouaisian canons established the abbey in 1138, and secondly, the work includes dedicatory prayers to Peter and Paul, the patrons of Bourne Abbey. The Arrouaisian rule was largely that of Augustine, so that its houses often are loosely referred to as Augustinian.

Scholars cannot pinpoint the exact date of composition. Orrm wrote his book over a period of decades and the manuscript shows signs of multiple corrections through time. Since it is an autograph, with two of the three hands in the text generally believed by scholars to be Orrm's own, the date of the manuscript and the date of composition would have been the same. On the evidence of the third hand (that of a collaborator who entered the pericopes at the head of each homily) it is thought that the manuscript was finished c. 1180, but Orrm may have begun the work as early as 1150. The text has few topical references to specific events that could be used to identify the period of composition more precisely.

Manuscript
Only one copy of the Ormulum exists, as Bodleian Library MS Junius 1. In its current state, the manuscript is incomplete: the book's table of contents claims that there were 242 homilies, but only 32 remain. It seems likely that the work was never finished on the scale planned when the table of contents was written, but much of the discrepancy was probably caused by the loss of gatherings from the manuscript. There is no doubt that such losses have occurred even in modern times, as the Dutch antiquarian Jan van Vliet, one of its seventeenth-century owners, copied out passages that are not in the present text. The amount of redaction in the text, plus the loss of possible gatherings, led J. A. W. Bennett to comment that "only about one fifth survives, and that in the ugliest of manuscripts".

The parchment used in the manuscript is of the lowest quality, and the text is written untidily, with an eye to economical use of space; it is laid out in continuous lines like prose, with words and lines close together, and with various additions and corrections, new exegesis, and allegorical readings, crammed into the corners of the margins (as can be seen in the reproduction above). Robert Burchfield argues that these indications "suggest that it was a 'workshop' draft which the author intended to have recopied by a professional scribe".

It seems curious that a text so obviously written with the expectation that it would be widely copied should exist in only one manuscript and that, apparently, a draft. Treharne has taken this as suggesting that it is not only modern readers who have found the work tedious. Orrm, however, says in the preface that he wishes Walter to remove any wording that he finds clumsy or incorrect.

The provenance of the manuscript before the seventeenth century is unclear. From a signature on the flyleaf we know that it was in van Vliet's collection in 1659. It was auctioned in 1666, after his death, and probably was purchased by Franciscus Junius, from whose library it came to the Bodleian as part of the Junius donation.

Contents and style
The Ormulum consists of 18,956 lines of metrical verse, explaining Christian teaching on each of the texts used in the mass throughout the church calendar. As such, it is the first new homily cycle in English since the works of Ælfric of Eynsham (c. 990). The motivation was to provide an accessible English text for the benefit of the less educated, which might include some clergy who found it difficult to understand the Latin of the Vulgate, and the parishioners who in most cases would not understand spoken Latin at all.

Each homily begins with a paraphrase of a Gospel reading (important when the laity did not understand Latin), followed by exegesis. The theological content is derivative; Orrm closely follows Bede's exegesis of Luke, the Enarrationes in Matthoei, and the Glossa Ordinaria of the Bible. Thus, he reads each verse primarily allegorically rather than literally. Rather than identify individual sources, Orrm refers frequently to "ðe boc" and to the "holy book". Bennett has speculated that the Acts of the Apostles, Glossa Ordinaria, and Bede were bound together in a large Vulgate Bible in the abbey so that Orrm truly was getting all of his material from a source that was, to him, a single book.

Although the sermons have been deemed "of little literary or theological value" and though Orrm has been said to possess "only one rhetorical device", that of repetition, the Ormulum never was intended as a book in the modern sense, but rather as a companion to the liturgy. Priests would read, and congregations hear, only a day's entry at a time. The tedium that many experience when attempting to read the Ormulum today would not exist for persons hearing only a single homily each day. Furthermore, although Orrm's poetry is, perhaps, subliterary, the homilies were meant for easy recitation or chanting, not for aesthetic appreciation; everything from the overly strict metre to the orthography might function only to aid oratory.

Although earlier metrical homilies, such as those of Ælfric and Wulfstan, were based on the rules of Old English poetry, they took sufficient liberties with metre to be readable as prose. Orrm does not follow their example. Rather, he adopts a "jog-trot fifteener" for his rhythm, based on the Latin iambic septenarius, and writes continuously, neither dividing his work into stanzas nor rhyming his lines, again following Latin poetry. Orrm was humble about his oeuvre: he admits in the preface that he frequently has padded the lines to fill out the metre, "to help those who read it", and urges his brother Walter to edit the poetry to make it more meet.

A brief sample may help to illustrate the style of the work. This passage explains the background to the Nativity:

Orthography
Rather than conspicuous literary merit, the chief scholarly value of the Ormulum derives from Orrm's idiosyncratic orthographical system. He states that since he dislikes the way that people are mispronouncing English, he will spell words exactly as they are pronounced, and describes a system whereby vowel length and value are indicated unambiguously.

Orrm's chief innovation was to employ doubled consonants to show that the preceding vowel is short and single consonants when the vowel is long. For syllables that ended in vowels, he used accent marks to indicate length. In addition to this, he used three distinct letter forms for the letter g depending on how they sounded. He used insular <ᵹ> for the palatal approximant, a flat-topped <ꟑ> for the velar stop , and a Carolingian  for the palato-alveolar affricate , although in printed editions the last two letters may be left undistinguished. His devotion to precise spelling was meticulous. For example, he originally used eo and e inconsistently for words such as beon and kneow, which had been spelled with eo in Old English. At line 13,000 he changed his mind and went back to change all the eo spellings in the book, replacing them with e alone (ben and knew), to reflect the pronunciation.

The combination of this system with the rigid metre, and the stress patterns this meter implies, provides enough information to reconstruct his pronunciation with some precision; making the reasonable assumption that Orrm's pronunciation was in no way unusual, this permits scholars of the history of English to develop an exceptionally precise snapshot of exactly how Middle English was pronounced in the Midlands in the second half of the twelfth century.

Significance
Orrm's book has a number of innovations that make it valuable. As Bennett points out, Orrm's adaptation of a classical metre with fixed stress patterns anticipates future English poets, who would do much the same when encountering foreign language prosodies. The Ormulum is also the only specimen of the homiletic tradition in England between Ælfric and the fourteenth century, as well as the last example of the Old English verse homily. It also demonstrates what would become Received Standard English two centuries before Geoffrey Chaucer. Further, Orrm was concerned with the laity. He sought to make the Gospel comprehensible to the congregation, and he did this perhaps forty years before the Fourth Council of the Lateran of 1215 "spurred the clergy as a whole into action". At the same time, Orrm's idiosyncrasies and attempted orthographic reform make his work vital for understanding Middle English. The Ormulum is, with the Ancrene Wisse and the Ayenbite of Inwyt, one of the three crucial texts that have enabled philologists to document the transition from Old English to Middle English.

title: Ormulum


text:
County-level city

A county-level municipality, county-level city or county city, formerly known as prefecture-controlled city (1949–1970: ; 1970–1983: ), is a county-level administrative division of the People's Republic of China. County-level cities have judicial but no legislative rights over their own local law and are usually governed by prefecture-level divisions, but a few are governed directly by province-level divisions.

A county-level city is a "city" and "county"  that have been merged into one unified jurisdiction. As such, it is simultaneously a city, which is a municipal entity, and a county, which is an administrative division of a prefecture. Most county-level cities were created in the 1980s and 1990s by replacing denser populated counties.

County-level cities are not "cities" in the strictest sense of the word, since they usually contain rural areas many times the size of their urban, built-up area. This is because the counties that county-level cities have replaced are themselves large administrative units containing towns, villages and farmland. To distinguish a "county-level city" from its actual urban area (the traditional meaning of the word "city"), the term "市区" (shìqū) or "urban area", is used.

Comparable territorial divisions in other countries
While the idea of a "city" being a unit consisting of several "towns" is not a common one in English-speaking world, a somewhat similar naming convention is used for local government areas in some parts of Australia. For example, in New South Wales such a unit may often be called a "city" (rather than a traditional "shire"), and consist of "towns". E.g. City of Blue Mountains is made of a number of towns (Katoomba, Springwood, etc.).

List
As of 3 April 2023, there are 408 county-level cities in total:

Sub-prefectural cities
A sub-prefectural city is a county-level city with powers approaching those of prefecture-level cities. Examples include, Xiantao (Hubei), Qianjiang (Hubei), Tianmen (Hubei) and Jiyuan (Henan).

title: County-level city


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The Worst Witch

The Worst Witch is a series of children's books written and illustrated by Jill Murphy. The series are primarily about a girl named Mildred Hubble who attends a witch school and fantasy stories, with eight books published. The first, The Worst Witch, was published in 1974 by Allison & Busby, and the most recent, First Prize for the Worst Witch, was published in 2018 by Puffin Books, the current publisher of the series. The books have become some of the most successful titles on the Young Puffin paperback list and have sold more than 5 million copies.

In 1986, the first book in the series was made into a television film of the same name. A TV series based on the book aired from 1998 to 2001, and has inspired two spin-offs, Weirdsister College, aired in 2001, and The New Worst Witch, aired in 2005. Another adaptation premiered in 2017.

Background
The author Jill Murphy began writing The Worst Witch at the age of 15, while still at school, and based many points of the stories on her own school experiences at Ursuline Convent in Wimbledon, England, with Singing becoming Chanting, Chemistry becoming Potions and so on. Recalling how the story was initially inspired by her own school experiences, she said in an interview: "My two friends and I used to come home in our dark uniforms, looking very scruffy at the end of the day – my dark plaits sprouting tufts, with lost hair ribbons. My Mum used to say 'Look at you all. You look like the three witches!' and it gave me the idea for a witch's school – so that it was exactly like my school, but with a subtle touch of magic. All the characters are based on my school friends (and enemies) and teachers".

Murphy concluded the first book at the age of 18, but it was rejected by many publishers (on the grounds that children would find a book about a school for witches too "scary"), so she "put it in a drawer" and concentrated on other things, including working as a nanny and in a children's home, and for a time living in West Africa, where her first husband was studying.

Publication of The Worst Witch finally came about, as Jill Murphy recalled, "thanks to a series of coincidences involving me spending time in Ghana, and a friend meeting Margaret Busby (Ghanaian herself, and considering starting a children's list for her imprint) at a publishers' party in London". The Worst Witch was finally published in 1974, when Murphy was 24, by the small independent company Allison and Busby.

Series overview
The books in the series all focus on Mildred Hubble, a young witch who attends Miss Cackle's Academy for Witches, a school of magic. Although well-intentioned, Mildred's clumsy personality leads the girl to disastrous situations, and she is thus considered the worst student in the school. The benevolent headmistress, Miss Cackle, is generally understanding, whereas Mildred's form teacher Miss Hardbroom thinks she just isn't trying hard enough. Mildred's friends include Maud Spellbody, a rotund, sensible girl who is always trying to avoid confusion, and Enid Nightshade, a practical joker who is more likely than Mildred to get them all into trouble. The three girls have a strong rivalry with Ethel Hallow, a high-born, snobbish and vindictive classmate.

Each book covers one term at the school. There are two terms each year: the Winter term, from September to January, and the Summer term, from March to July. In First Prize for the Worst Witch, the most recent book, Mildred is in the Summer term of her fourth year.

The Worst Witch
The Worst Witch was first published in 1974 by Allison & Busby, and proved to be an immediate success, selling out within two months.

The novel begins with Mildred Hubble and the upcoming traditional assembly where all of the first-years are given their own black cats that they will teach to ride on their broomsticks with them. Unlike the other girls, who receive black kittens, Mildred receives a tabby cat, which she simply calls Tabby. The kitten is unable to sit on a broomstick, so Mildred carries Tabby in her bag. Miss Hardbroom disapproves, and Mildred has to stop. Afterwards, another witch called Ethel Hallow teases Mildred about it and dares her to turn her into a frog. Mildred loses her temper and turns Ethel into a pig instead.
 * Plot

In the next chapter, Mildred and Maud inadvertently make an invisibility potion instead of a laughing potion in their class test.

In the following chapter, the girls are practising for a broomstick display for Halloween. Ethel lends Mildred her spare broom, on which she has secretly put a spell. During the Halloween festival, Mildred's broom starts bucking, causing all the girls to fall from their broomsticks. The Chief Magician denounces the academy, and Mildred is summoned to a meeting with Miss Cackle and Miss Hardbroom the next morning. Mildred, fearing expulsion, decides to run away with Tabby.

When walking through the forests near the academy, Mildred hears voices through the trees and comes across a group of witches, headed by one who looks like Miss Cackle. After hearing their plot to turn every teacher and student witch in the academy into frogs, Mildred turns the group into snails, packs them into cardboard boxes, and takes them back to the academy. At first, Miss Cackle and Miss Hardbroom refuse to believe her, but when Mildred describes the leader, Miss Cackle realises she sounds like her identical twin sister, Agatha. They turn Agatha and her associates back into humans. Mildred's interview is cancelled for saving the school. Later that morning, Ethel is exposed as the cause of Mildred's broomstick mishap, and Mildred is vindicated and praised as a hero to the rest of the academy.

The Worst Witch Strikes Again
The Worst Witch Strikes Again was first published in 1980 by Allison & Busby and features a new character, Enid Nightshade.

Mildred Hubble returns to Miss Cackle's Academy for Witches for the Summer Term of her first year. Miss Cackle has trusted Mildred to look after the new girl, Enid Nightshade, and help her settle in. Because Mildred has to spend a lot of time with Enid, Maud becomes angry and jealous and breaks off their friendship, siding with Ethel in retaliation.
 * Plot

Mildred starts showing Enid around the academy, only to discover that Enid has smuggled a monkey into school with her. During the assembly that follows, Miss Cackle announces her birthday celebration. During a chanting lesson with Miss Bat after assembly, Enid deliberately sings awkwardly and out of tune, causing Mildred to burst into laughter. Mildred is sent to Miss Cackle's office. When going up to her room, Mildred checks on Enid's monkey, causing it to escape. Mildred chases it down the stairs and bumps into Miss Hardbroom, who sends her to the library to study.

After spotting the monkey on top of one of the castle towers, Mildred jumps onto her broomstick. Miss Hardbroom turns the monkey into its original form, a school regulation black cat. Enid secretly reveals to Mildred that she turned the cat into a monkey for fun.

On Sports Day, Mildred and Enid become partners. Enid places a spell on Mildred's pole, so in the pole-vaulting contest, Mildred springs high into the air and lands into Miss Hardbroom's study via the window. Moments later, Miss Cackle, Miss Hardbroom, and Miss Drill arrive, and Miss Cackle angrily says that if there is any more bother from Mildred that term, she will be expelled.

Determined to avoid expulsion for the rest of the term, Mildred refuses every daring suggestion Enid makes. Enid decides to skip Miss Cackle's boring birthday celebration and hides in a store cupboard, pulling Mildred in with her. Seeing an opportunity to get Mildred expelled, Ethel Hallow spitefully locks the door behind them.

Inside the cupboard, the two girls find an old broomstick that they use to fly out of a slit-window leading into the assembly hall. As luck has it, Maud is on stage, having been chosen to recite the first years' contribution to the recital. Having long regretted her jealous behaviour, Maud introduces Mildred and Enid as a surprise broomstick display item. The display doesn't go especially well, but Miss Cackle decides it is the thought and effort that counts and praises them highly. The three girls become friends and are delighted when the end-of-term bell rings with Mildred still a pupil at the academy.

A Bad Spell for the Worst Witch
A Bad Spell for the Worst Witch (ISBN 978-0-7226-5763-8) was published in 1982. It features Ethel Hallow's little sister, Sybil Hallow, and her friend Clarice Crow.

Mildred Hubble returns to Miss Cackle's Academy for Witches for her second year, determined to lose her embarrassing reputation as "the worst witch in the school". After Maud Spellbody and Enid Nightshade arrive, the three bump into two first-years (one of whom reminds Mildred very strongly of someone, the other with ginger frizzy hair in bunches). The one who seems familiar bursts into tears and clings onto Mildred when she hears that many of the teachers (including Miss Hardbroom) are quite strict. Mildred also accidentally slips a made-up story about Miss Hardbroom turning a student into a frog when she was just two seconds late for a lesson. To the girls' horror, they also learn that they have Miss Hardbroom for another year.
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The next morning, a fire bell rings. Mildred scrambles into her clothes, notices from her window that Miss Hardbroom standing in the playground surrounded by hazy purple smoke. Thinking she is in a state of shock, Mildred tries to douse her in freezing cold water, but the bucket slips off her broomstick and lands with a clang on Miss Hardbroom's head. After witnessing the incident, Ethel Hallow confronts Mildred at lunchtime, saying that the girl she told the frog story to was her younger sister, Sybil. After much provocation, Mildred loses her temper and insults Ethel's family —"All you Hallows are weeds, weeds, weeds!"

After an unfortunate flying lesson, where Tabby makes another terrified attempt to avoid sitting on the end of the broomstick, Miss Hardbroom sends Mildred to her room to calm down. When sitting in her bed, however, Mildred accidentally falls asleep and does not hear Ethel creeping into her room.

Mildred is awoken by her bedroom door shutting, only to find that everything looks giant-sized, even Tabby. Peeking in the mirror, she finds that somebody has turned her into a frog. When jumping onto her bed, the frog-Mildred notices a tatty handful of weeds on her pillow, no doubt left by Ethel as a reference to her family's insult and why she turned her into the frog.

Panicking, Mildred squeezes under the gap under her bedroom door and hops off to a potions lesson, where everyone has noticed her disappearance. Miss Hardbroom, however, discovers her and puts her in a jar. During the lesson, Mildred manages to escape from the jar and hops over to Ethel's desk, where she drinks an invisibility potion. Taking advantage of her invisibility, the frog-Mildred hops out of the academy and lands in the lily pond on the castle grounds.

There, Mildred meets another frog who was also a human once called Algernon Rowan-Webb (though he has been a frog for so long he can barely remember his surname). Algernon reveals that, rather like Mildred, he was turned into a frog by a fellow magician after an argument and can only be turned back into a human by another magician. Algernon also reveals that the one thing he craves is to have a "proper tea again, with buttered toast and crumpets with honey".

Promising to return for him, Mildred hops back up to the academy. Maud and Enid, who have been worrying about their friends' disappearance, suddenly realise what has happened when Tabby shows affection towards the frog-Mildred, and take her to Ethel, who reluctantly turns her back into a human. Miss Hardbroom comes by, and Ethel tells her that she caught Maud, Enid, and Mildred sneaking around the school. Mildred furiously attempts to tell the truth, and the disbelieving Miss Hardbroom is about to give her a punishment when she notices that Mildred's feet are still invisible. Mildred realises that this proves her story and tells Miss Hardbroom what happened in the potion lab. Miss Hardbroom tells Mildred and Ethel to report to her office the next day.

In the morning, Miss Hardbroom reprimands both Mildred and Ethel for their ongoing feud, and they are both punished with lines – Ethel for turning Mildred into a frog and attempting to lie her way out of trouble, and Mildred for upsetting Ethel's sister. The two girls are also banned from attending the Halloween ceremonies – the only chance Mildred would have had to find a magician who could turn Algernon back into a human. Mildred feels she has no choice but to kidnap somebody who is going to the Halloween festival. She tricks a third-year witch, Griselda Blackwood, into looking under her bed for an imaginary beetle before tying her up and taking her cat.

Later, Ethel discovers Griselda being held captive in Mildred's room, and the two fly off to the festival to turn Mildred in. When exposed, Mildred takes the plunge and strides up to chief magician Mr Hellibore, handing him the box that contains Algernon. As luck would have it, Mr Hellibore was one of Algernon's fellow magicians at the time of his transformation, and he immediately turns him old friend back to his human form.

As a last request from Mildred, Mr Hellibore magics up a pot of tea and a plate of toast, crumpets, and butter. Algernon himself then conjures a pot of honey for the crumpets and the three head off to enjoy the supper.

The Worst Witch All at Sea
The Worst Witch All at Sea (ISBN 978-0-670-83253-8) was published in 1993. It is the only book in the series not set in Miss Cackle's Academy for Witches, but by the sea instead.

Mildred Hubble returns to Miss Cackle's Academy for Witches for the Summer Term of her second year. Instead of the usual black-and-grey-checked dresses, Miss Hardbroom persuaded Miss Cackle to change them to plain black. After crash-landing in a pile of snow and meeting up with her best friends, Maud Spellbody and Enid Nightshade, Ethel Hallow appears and tells Mildred that Miss Cackle wants to see her.
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Miss Cackle suggests to Mildred that she replaces Tabby. Last term, a third-year witch, Fenella Feverfew, transferred to Miss Pentangle's Academy several mountaintops away and left behind her sleek black cat, Ebony, since they have owls at Miss Pentangle's instead of black cats. Down in the kitchens, Mildred reluctantly hands over Tabby to Miss Tapioca (to catch mice), who gives her Ebony in return. Mildred is too upset to tell either Maud or Enid about it until after assembly.

Miss Hardbroom announces that Mr Rowan-Webb, the frog-magician whom Mildred saved from the lily pond the previous term, has invited all the second-years to spend a week's holiday at his castle, Gloom Castle at Grim Cove.

On the morning of departure, unable to bear the thought of a week without Tabby, Mildred sneaks down into the school kitchens, lets Ebony out of his cage, and instead hides Tabby inside.

When they reach Gloom Castle, they find that it is falling apart: the armchairs have springs and stuffing sticking out and there are no proper beds (apart from one, which Ethel Hallow immediately claims) other than old sleeping-bags, piles of pillows, and what appear to be hospital trolleys. Mildred gets an old sleeping-bag under the window and realises she must divert attention away from Tabby.

Mildred spots a boat attached to a breakwater and decides to hide Tabby in the cabin of the boat. After a wonderful day on the beach, Mildred tries to sneak some kippers to Tabby, but Ethel catches Mildred, who pretends to be looking for some mythical treasure on Cat's Head Rock in front of the cove in the boat on the breakwater. As the two head back up the cliff stairs, they witness Miss Hardbroom flying down to the beach on her broomstick with her own black cat, Morgana. Morgana runs to the boat and feeds on the kippers that were meant for Tabby. Miss Hardbroom spots both Tabby in the cabin and Morgana eating the fish. Stepping on board to investigate, she slips on a kipper, hits her head, and falls unconscious.

Sneaking out to feed Tabby again, Mildred is confronted by Ethel, who snidely tells her that she has untied the boat and let it drift out to sea. Mildred uses a broomstick that she finds on the beach (not realising it is Miss Hardbroom's) to fly out to the drifting boat, where she discovers not only Tabby but the comatose Miss Hardbroom. Minutes after, they bump into Cat's Head Rock. Mildred ties the boat onto an odd-looking chunk of rock and falls asleep.

When she awakens, she finds that Maud and Enid have discovered them. Mildred tells them that there is something strange about the rock the boat is tied to. They pull at it and find that it is the mythical treasure chest. When they get back, Miss Hardbroom has revived, and her injured head is bandaged. The contents of the treasure chest are used both to repair Gloom Castle and to refurbish Cackle's Academy, and Mildred is permitted to keep Tabby again as a reward.

Mildred enjoys the rest of her holiday, feeling like "the luckiest girl in the world instead of the worst witch in the school".

The Worst Witch Saves the Day
The Worst Witch Saves the Day (ISBN 978-0-14-138218-0) was published in 2005. It features Agatha Cackle disguised as new teacher Miss Granite.

Mildred Hubble is returning to Miss Cackle's Academy for Witches on the first day of her third year. After meeting up with her friends, Maud Spellbody and Enid Nightshade, Mildred sees that Maud's hair is curly (she borrowed a hairstyling brush from her aunt) and they also learn that they will have a new form-teacher this year other than Miss Hardbroom.
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They see in assembly that their new form-teacher will be Miss Granite, who was hired by Miss Cackle after Miss Gribble failed to show discipline and against Miss Hardbroom's advice. Miss Granite is described as being very strange-looking and having "a huge cloud of orange curls" and also wearing "enormous purple-tinted glasses and a short cape with a collar turned up so high that you couldn't see much of her face at all". Miss Granite speaks in a very high-pitched, squeaky voice that shocks everyone, including Ethel Hallow.

Mildred unravels her pigtails to try out Maud's styling brush. Maud and Enid find her with her hair loose, and a chunk of her hair tangled up with the brush in a huge mess. Ethel comes in and volunteers to help. However, the "help" amounts to taking a pair of scissors and chopping off both the styling brush and the messy hair.

Ethel later offers to help Mildred again in her hair predicament. She formulates a potion that she claims will restore Mildred's hair to its rightful length. Mildred applies the potion that night, and just when she is dropping off to sleep, her hair starts growing longer and longer by the minute, engulfing the whole school. Miss Hardbroom comes to investigate, states that Mildred is having "a bad hair day", manages to stop the hair growing and cuts it to its rightful length and vapourises the swathes of hair that had engulfed the whole school.

In a flying lesson, Ethel steals Tabby (who has been suffering a nervous breakdown as a result of the hair incident) and hides him on the roof in front of Miss Granite's study's window.

That night, when trying to recover Tabby, Mildred is locked in a cupboard by someone who seems to be Miss Cackle but is actually Miss Cackle's identical twin Agatha Cackle, who sneaked into the school disguised as Miss Granite. Agatha is trying to turn all the teachers and pupils into snails. Mildred manages to turn herself into an ant, sneaks out of the cupboard, and goes to Maud's room, where she tries unsuccessfully to wake her. Fortunately, she is able to attract Maud and Enid's attention by using ink-blots to write two notes – "HELP NOT ANT" attracting their attention to her and "FORGOT SPEL" clarifying her dilemma – and Maud and Enid turn her back into a human. Mildred tells them what is going on, and just as Agatha is about to turn Miss Cackle into a snail, Mildred turns her into a snail herself. They also bump into Miss Hardbroom, who had been away.

Miss Hardbroom suggests that Miss Cackle poses as Agatha and invites Agatha's rebellious coven in, whereupon Mildred and the others will turn them all into snails, which happens. As Mildred, Maud, and Enid go back to bed, they realise that they miss Miss Hardbroom as their form-teacher. She suddenly appears in front of them and is friendly for a brief moment, admitting she has missed them too, before strictly telling them to get back to bed with no candles on.

The Worst Witch to the Rescue
The Worst Witch to the Rescue (ISBN 978-0-14-138301-9) was published in 2007 and features Ethel Hallow's only friend, Drusilla Paddock, in a largely increased role since her brief cameo in The Worst Witch All at Sea.

Ethel Hallow is returning to Miss Cackle's Academy for Witches for the Summer Term of her third year. Miss Hardbroom had previously set them a holiday project, but Ethel is doing exactly what Miss Hardbroom told them not to do: trying to think up a project in five minutes flat on the way back to school. Ethel spots Mildred Hubble crash-landed in a tree and manages to help her steady herself. Mildred explains to Ethel her project: a spell that can make animals talk, though it can only work on animals that fit into 25 centimetres and only lasts for two weeks. When helping Mildred out of the tree, Ethel knocks Mildred's luggage out of the tree. While Mildred tries to get Tabby, who had scampered up the tree, Ethel scoops up Mildred's project folder and art bag and her 30 coloured pencils.
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On the way there, Mildred finds her friends Maud Spellbody and Enid Nightshade. When Mildred tells them about Ethel being nice for a change, Enid suggests she may have taken a "niceness course" during the holidays. Maud and Enid become suspicious when they catch Mildred talking to someone or something in her cat basket.

The girls find that their new form mistress is called Miss Mould, who has a "soft and kindly" voice and "short mousy hair parted in the middle and pulled into a ponytail at her neck". She is a great relief from the horrifically strict Miss Hardbroom and the extremely weird Miss Granite whom they had had the previous term. Mildred sits next to Drusilla Paddock, who swaps places with Ethel after Miss Mould tells Ethel her coils are too short. Minutes later, a maraca-like noise echoes through the classroom. Mildred finds that her coils have turned into five rattlesnakes. Miss Mould gets the whole class outside while Ethel stays inside and evaporates the rattlesnakes. Just then, Miss Hardbroom appears, and Miss Mould explains what happened. Miss Hardbroom sends Mildred to her room and bans her from art lessons for the rest of the term. Mildred runs to her room, where she figures out it must have been Ethel, who turned her pot and coils into the snakes out of jealousy. The next day, in a lesson with Miss Hardbroom, the girls are presenting their projects to the class. Ethel goes first, but her project is the same as Mildred's. Mildred shouts to Miss Hardbroom that Ethel had stolen her project. Miss Hardbroom opens Mildred's project folder but finds only many sheets of paper with smiley faces drawn on them in different colours. Miss Hardbroom "transfers" Mildred to her room.

Later, Mildred finds that the creature inside her cat basket, a tortoise called Speedy whom she had used her spell on, can still speak. She renames him Einstein, and he tells her about overhearing her conversation with Ethel inside the tree. After Mildred runs to tell Maud and Enid the good news, Mildred accidentally leaves her bedroom door open, and Einstein escapes. While plodding along the corridor, he is discovered by Drusilla Paddock, who takes him to Ethel's room. While Ethel and Drusilla talk, it is revealed that Ethel did indeed take Mildred's project and had also "tried out" a snake spell on Mildred's pot and coils in art. Einstein overhears everything.

When they are taking Einstein back to Mildred, Ethel eavesdrops on what Mildred is telling Maud and Enid. After discovering that Einstein can still speak and had overheard the conversation between Ethel and Mildred about the project, and that Einstein only has one more day before the spell wears off and he becomes mute forever, Ethel orders Drusilla to hide Einstein in the hollow pine tree outside the school gates. Einstein is put into a cardboard box that also contains a small green frog called Cyril, the animal whom Ethel had used in her demonstration. Cyril escapes and hops to Mildred's room. Cyril tells Mildred that Drusilla hid Einstein in the hollow pine tree outside the school gates and that he overheard several conversations about stealing projects and turning pots into snakes.

After releasing Cyril into the woods, Mildred gets on her broomstick and, during a violent thunderstorm, finds and rescues Einstein. On landing, she is confronted by Miss Hardbroom, who takes Mildred and Einstein inside and, after hearing part of the incidents from Mildred, sets an interview with Mildred and Ethel the next morning.

The next morning, Mildred goes to Miss Cackle's office where Einstein, resting in Miss Cackle's overflowing in-tray, awakes and tells Miss Cackle and Miss Hardbroom that he overheard the conversation between Ethel and Mildred in the tree. He also says that he heard Ethel telling Drusilla that she had tried out a snake spell on Mildred's coils and had taken Mildred's project, copied it out in her own writing, and then thrown it in the kitchen bins. Ethel sifts through the rubbish and eventually finds Mildred's tea-stained project. Miss Hardbroom makes Ethel apologise to Mildred in assembly in front of the whole year as an alternative to being expelled for cheating as well as for her actions that put herself and Mildred in great danger.

During a broomstick-flying lesson, Mildred reveals to Maud and Enid that Miss Cackle had provided Miss Mould's classroom with a proper kiln and craft room and she also got to keep Einstein as a pet. As the clock strikes midday, Mildred sprints into her room and hears Einstein speak for the last time in his raspy little voice ("I'm glad I belong to you"), before munching on his carrot and going silent forever.

The Worst Witch and the Wishing Star
The Worst Witch and the Wishing Star (Scholastic UK, ISBN 978-0-141351995; another (?), ISBN 978-0-141383996) was released by Scholastic UK in 2013.

Returning from the holidays in stormy weather Mildred, Maud and Enid arrive to be told by Miss Drill that there will be a talent-displaying competition between Miss Cackle's Academy, Moonridge and Pentangle's school to win a swimming-pool as the award for the best talent.

Mildred, much to her disappointment, has been chosen to work lantern monitor along with Drusilla and Ethel. On that first night, Maud spots a shooting star, and Mildred makes a wish, followed by Miss Hardbroom, who does the same reluctantly. On the first lantern monitor shift, Mildred is given a holdall containing safety objects in it. When she reaches the gates to finish the job, Mildred spots a stray dog, who she names Star. She takes him to her bedroom as a secret pet, much to the disapproval of Tabby.

During the weeks that follow Mildred, realising that Star is well behaved and calm on a broomstick, she trains him to do various tricks with her. Maud and Enid, who realise Mildred isn't spending much time with them, soon discover about Star and are amazed by the tricks Mildred has taught him. Ethel, suspicious about Mildred hiding something in her holdall, reaches into it to discover Star was hidden in it and the both of them collapse into the lanterns igniting the costumes Form Five have made for the talent competition.

Miss Hardbroom, furious, sends Ethel and Mildred along with Star on a lead to Miss Cackle's office for what they had done. Maud and Enid then explain about Star's tricks on the broom. Miss Cackle accepts the replacing talent, and the next day, the competition took place with the schools showing their talents. When it's Mildred's turn, she amazes the judges with Star's tricks and wins the competition and the swimming pool. When the pupils go back to their school, Miss Cackle allows Mildred to keep Star as her broomstick companion as a special privilege. Mildred later explains to Miss Hardbroom that she wished for Star on the shooting star at the beginning of term, which doesn't annoy her as she wished on the star for them to win the competition. The story concludes with the teachers celebrating their victory and, at the same time, Miss Hardbroom's birthday.

First Prize for the Worst Witch
First Prize for the Worst Witch (ISBN 9780141355092) was published in 2018. Its writing was delayed when Murphy underwent cancer treatment.

Heading back to Miss Cackle’s Academy at the start of the summer term of the fourth year, Mildred is feeling much more confident thanks to her new broomstick companion, Star the dog, new-found flying skill, and recent successes such as winning a swimming pool for the school. She confesses to Maud that she even dreams of being selected as Head Girl for next year at the end-of-term prizegiving, though they both concede it seems incredibly unlikely; even without considering Mildred's long career of mishaps, they find it impossible to imagine anyone but Ethel Hallow taking the position. Not only is Ethel academically easily the strongest member of her year, but every member of the Hallow family to attend the school for the past two centuries has held the position of Head Girl.

However, Mildred quickly discovers that her nemesis Ethel Hallow has gotten hold of a flyer from a local circus that suggests that her pet Star is their lost property, and has given it to Miss Cackle and Miss Hardbroom. The teachers tell Mildred that they have no choice but to contact the circus and, if necessary, return the dog. When the circus owners, Mr and Mrs Brilliantine, arrive, they confirm that Star is their missing circus dog Binky, and Mildred is devastated to have to turn her beloved dog over to them, particularly as it is clear that he desperately wants to stay with Mildred.

Losing the talented Star and having to return to using the terrified Tabby as her broom companion ruins Mildred’s recent flying skills, and with her confidence shattered she also sinks back to her previous position at the bottom of most of her classes. After several months she sneaks out very early one morning along with Enid and Maud to go find Star at the Brilliantines’ circus and see how he is doing. Star’s excited barking at seeing Mildred wakes the Brilliantines, who understand why Mildred would want to visit her former pet, and give the girls a tour of their circus. As well as Star the circus features a horse and a seal. The Brilliantines concede that the circus life is hard on the animals, but that they can’t give them up, as without them they would have lost most of their acts.

Mildred makes a second visit on her own with the purpose of casting the animal-speaking spell she previously invented on all three animals, all of whom beg her to take them away from the circus. She promises them that she will, but it is weeks before Enid hits of the idea of offering the Brilliantines a set of enchanted brooms and brushes to use in their acts instead of the animals. The Brilliantines love the magical items, and cheerfully sign the animals over to Mildred, who attempts to teleport the seal to her colony in Grim Cove (though she accidentally teleports it to the school’s new swimming pool, and Miss Hardbroom has to remedy this later), and takes Star and the horse Merlin back to school.

At school Mildred tries to convince Miss Cackle and Miss Hardbroom to let her keep Star and for the school to adopt Merlin. Ethel complicates matters by telling the teachers about how Mildred and her friends traded enchanted items for them, hoping to get Mildred in trouble both for stealing school property and for ‘trivial usage of magic’. Ultimately, though, Miss Cackle convinces Miss Hardbroom that using magic to find a way to free her pet and other animals from an unpleasant life of servitude could hardly be considered ‘trivial’, and that Mildred’s inventiveness and determination to solve problems are attributes that should not be overlooked…

At the final day of term’s prizegiving event for Fourth Years Ethel unsurprisingly sweeps all of the academic awards, though Maud manages to win the prize for Team Spirit, which delights her and the entire school (aside from Ethel). However, when it comes to the award for Head Girl everyone is shocked when Miss Cackle announces that Mildred Hubble will be next year’s Head Girl. When she finally gets over her amazement Mildred picks Enid to be her deputy. After prizegiving ends and the girls prepare to head home, Mildred, Maud and Enid are shocked once again when Miss Hardbroom congratulates them personally, albeit in her own acerbic manner.

Setting
The stories mainly take place within the walls of Miss Cackle's Academy for Witches, a girls-only boarding magic school that is described in the books as a stone castle on top of a mountain, surrounded by pine forest.

The school year is divided into two terms: the Winter term (September–January) and the Summer term (March–July), with a month's holiday between them. Students start at Cackle's at the age of 12 and finish at the age of 17 for a total of five school years. The students arrive at the start of the term by flying broomsticks, except for the new first years, who walk through the walker's gate as they can't fly yet. Halfway through the first term, the first years are each presented with a black kitten – Mildred receives a grey-and-black tabby cat as they apparently ran out of purely black cats – which they teach to ride the broomstick. The first book postulates that the cats weren't for any practical purpose except to keep tradition going, and in Wishing Star, a group of elder witches note that there is no restriction on what animal a witch must have as her flight companion, with cats only being traditional as they are discreet and easy to care for, which leads to Mildred being permitted to fly with her dog, Star, after he shows greater broom aptitude than her cat Tabby. At the end of the first year, each pupil receives a copy of The Popular Book of Spells, a three-inch thick volume bound in black leather. This was not really to be used, as they already had paperback editions for the classroom, but like the cats, it's another piece of tradition. At the end of the fifth and final year, students sit the exams for the W.H.C. (Witches' Higher Certificate), and most pupils were awarded with the certificate.

The first book says that the school winter uniform is composed of "black gymslips, black stockings, black hob-nailed boots, grey shirts and black-and-grey ties". The first book also postulates that "the only touches of colour [on the uniforms] were the sashes round their gymslips – a different colour for each house, although the houses are not named – and the school badge, which was a black cat sitting on a yellow moon". In the summer term, originally the girls wore grey-and-black checked dresses, but this was changed from Worst Witch All At Sea onwards to a simple black dress as Ms Hardbroom felt that the original design was too frivolous.

Television film
In 1986, the first book in the series was converted to a made-for-television film on ITV starring Fairuza Balk, Tim Curry, Diana Rigg, and Charlotte Rae. Though a British film, it also aired in the USA on HBO. The film followed the plot of the first book of the series, portraying the incidents of Mildred turning herself invisible and turning Ethel into a pig, Miss Cackle's evil twin sister Agatha plotting to take over the school, and the Grand Wizard viewing the Halloween Broomstick formation (sabotaged by Ethel's faulty broom she lent to Mildred). It was shot at St. Michael's College in Tenbury Wells. This holiday special later aired on the Disney Channel every year for Halloween until the late 1990s. Its opening song, "Growing Up Isn't Easy", was sung by Bonnie Langford; its music was composed by Charles Strouse and its lyrics were written by Don Black. Their other musical number was "Anything Can Happen on Halloween", sung by Tim Curry. Denis King composed its incidental music score and also wrote the song "My Little School".

Television series (1998–2001)
The Worst Witch, a TV series based on the books, starring Georgina Sherrington and Felicity Jones as Mildred Hubble and Ethel Hallow respectively, was broadcast from 1998 to 2001. It was shot in Montreal, London and Cardiff. The series is mostly shot in studio in London, with some episodes filmed in Montreal, Quebec, Canada. The exteriors of Cackle's Academy used Castell Coch, a castle located near Cardiff. The courtyard was filmed at Loseley Park, near Guildford. Inside the school (Great Hall, classrooms etc.) was filmed at Twickenham Studios.

Spin-offs
When it was no longer realistic that Mildred would still be at school, the series relocated her to a magical university in Cambridge and was retitled Weirdsister College: The Further Adventures of the Worst Witch and saw the return of Felicity Jones as a reinvented Ethel Hallow.

In 2004, a new series based on the 1998 series was made, entitled The New Worst Witch. It centred on the adventures of Mildred's equally bungling cousin, Henrietta "Hettie" Hubble, played by Alice Connor, also set at Cackle's Academy.

Television series (2017–2020)
A new version of The Worst Witch TV series began in 2017 airing on CBBC (later made available on Netflix) and concluded in 2020, this one starring Bella Ramsey as Mildred Hubble (replaced by Lydia Page in the fourth season so that Ramsey could focus on personal issues), Claire Higgins as Miss Cackle, and Raquel Cassidy as Miss Hardbroom.

Stage adaptation (2018–2019)
A musical stage production called The Worst Witch Live, adapted by Emma Reeves from Murphy's original books, was shown at the Royal & Derngate Theatre in Northampton from 27 November to 30 December 2018. In February 2019, the show began to tour the UK across 16 different venues. The Worst Witch Live by Kenny Wax Family Entertainment was shown at the Vaudeville Theatre in the West End from 24 July to 8 September 2019. The original cast included Danielle Bird, Polly Lister, Rachel Heaton, Rebecca Killick, Rosie Abraham, Anna Crichlow, Molly-Grace Cutler, Megan Leigh Mason, Emma Lau, and Meg Forgan.

This version is presented as a publicity play written by Mildred and acted out by the students and staff playing themselves, initially recreating Mildred's first year at school, although the second half takes on a metafictional angle as Agatha Cackle "infiltrates" the play and attempts to stage a coup of the magical government. The stage production received a 2020 Olivier Award for best family show.

title: The Worst Witch


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Sonic Animation

Sonic Animation (stylised as sonicanimation) are an Australian dance and techno musical group which was formed by Adrian Cartwright on keyboards, drums and programming and Rupert Keiller on lead vocals and programming in 1994. The group disbanded in 2006 and then reformed in 2011. Altogether, they have released five studio albums, Silence Is Deafening (May 1997), Orchid for the Afterworld (October 1999), Reality by Deception (2002), Defective Perspective (2004) and Once More from the Bottom (March 2013).

1994–1998: Formation and Silence Is Deafening
Sonic Animation were formed in Melbourne by Steve Bertschik as a DJ, Adrian Cartwright on drums, keyboards and programming and Canadian-born Rupert Keiller on lead vocals and programming in 1994. Cartwright on drums and Keiller on vocals were both members of Scarlet Garden, a rock group formed in the early 1990s in Geelong. The pair had met as employees at a local graphic design business.

Cartwright recalled "I absolutely hated dance music ... But Rupert took me to a rave, and that was it for me. I'd always thought that dance music was so minimalist and easy, but when you get into it it's actually quite intricate and complex. I loved that. And then when we heard what Underworld were doing with vocals, we wanted to do that, too." In 1995 Sonic Animation released their debut single, "Time Is an Illusion", on a self-funded independent label. They followed with "From Sand to Stars", Zero Zero Zero Zero One and Force Feed.

Their debut studio album, Silence Is Deafening, was issued on Azwan Transmissions in May 1997. All the tracks were written, produced and engineered by Sonic Animation. At that time they were using a 386 computer for programming. In March 2002 Keiller recalled how "people would yell out 'nice one 386!', cos you know, we didn't really do anything, it was all just the computer. There are still some people that hold that view but we don't see it as much because of the kind of shows we play these, days." Bertschik left the group in 1998 to "pursue his own musical interests." The band signed with a new label: Global Recordings / Festival / FIIDO.

1999–2005: Commercial success
In January 1999 the group issued a single, "Love Lies Bleeding", which reached the ARIA Singles Chart top 50. Jasper Lee of Oz Music Project felt that it "builds up into full blown dance goodness with no doubt an anthem to club culture with the main vocal". Its lyrics contain a reference to illegal drugs, "I feel ecstasy". This initially concerned Keiller "I used to be worried about that sort of stuff — I don't know why — but nothing so far has happened." "Theophilus Thistler" was released as a single in August 1999, which received high rotation on national radio station, Triple J, its popularity was assisted by the track's associated music video. The video featured their two mascots, or TechoTubbies, dubbed Robert Roley and Theophilus Thistler. At live performances the mascots' suits are worn by two fans selected by the band via their web site. "Theophilus Thistler" appeared on the ARIA Singles Chart top 100 and was listed at No. 18 on the Triple J Hottest 100, 1999, in a listeners poll.

The group's second studio album, Orchid for the Afterworld, was issued on 11 October 1999 on Global Records which peaked at No. 42 on the ARIA Albums Chart. In 2005 the album was certified gold for shipment of 35,000 copies by ARIA. Lee attended their gig in April 2000 at Macquarie University, he noticed "a weird mix of a rave and a mosh, with those up the front of the crowd firmly squashed in against the foldback speakers. Nonetheless everyone was having a great time, and enjoyed what Sonic Animation had to offer."

Sonic Animation's third studio album, Reality by Deception, was released on 4 February 2002, which peaked at No. 22 on the ARIA Albums Chart and No. 6 on the ARIA Dance chart. Lee felt the album "pares back the more commercially-friendly vocals... in favour of more straight trance-light tracks more akin to their clubbing roots... [They] have flowed with a different aim in mind that has seen a decent, although not terribly inspiring release." It provided the singles, "E-Ville" (October 2001), "I'm a DJ" (February 2002) and "Super Showbiz Star" (April 2002). "I'm a DJ" was listed at No. 74 on the Triple J Hottest 100, 2002.

Sonic Animation's fourth studio album, Defective Perspective was released on 9 February 2004, which provided the singles, "This Is not a Love Poem" and "Get Up". "This Is not a Love Poem" was based on lyrics by Philip Norton. Leasa de Klerk of InTheMix felt that the two CDs provided a "sheer variety of styles and sounds that are on the album. The guys are really showing their flexibility in their lastest offering."

Sonic Animation announced their break-up in mid-2005 with the release of compilation album, Eleven (September 2005), which appeared on the ARIA Dance Albums Chart top 25. It was followed by the Bugger Off tour. They made their last festival appearance at the Big Day Out in 2006 (Australian shows only).

2011–present: reformation and Once More from the Bottom
In 2011 Cartwright and Keiller revealed a new Sonic Animation remix for world music outfit, Delhi 2 Dublin. They announced that they were back in the studio recording their next album.

In March 2013, after an almost six-year hiatus, Sonic Animation released their fifth studio album, Once More from the Bottom. Adam Barbuto of Reverb noticed that "you get the feeling the lads from Sonic Animation have thrown their all into these songs and take this comeback super seriously. To somewhat refute any lack of confidence buyers may have had in the naming of the album, Once More from the Bottom, I can safely say SonicAnimation are anywhere near it. In fact I’d say they are back on track and heading for those big city lights." Rip It Up!'s Simone Keenan felt that "Although there’s plenty of odd-ball tracks ... there is some quality too like the hip hop/dubstep 'Punk on the Dance Floor' (which sounds better than the title may suggest) and 'Take It from Me' which features guest vocals from Canadian songstress Sexton Blake. Dub, techno, funk, house... You’ll find all of it on here." The album provided the single, "I Will Be Twisted"; its music video was created with fan-submitted footage taken on cell phones at the 2012 Homebake festival.

Members
Sonic animation are:
 * Adrian Cartwright
 * Rupert Keiller

with:

 * Steve Bertschik (circa 1994–1998)
 * Mark Saul (circa 1999–2001)
 * Richard Falkner (circa 2002–2004)
 * Erica Mclean (circa 2004–2006)
 * Sexton Blake aka Nadine Tremblay (circa 2012–2013)

ARIA Music Awards
The ARIA Music Awards is an annual awards ceremony that recognises excellence, innovation, and achievement across all genres of Australian music. Sonic Animation has been nominated for three awards.

 * 1999
 * "Love Lies Bleeding"
 * Best Dance Release
 * Nominated
 * rowspan="2"| 2000
 * rowspan="2"| Orchid for the Afterworld
 * Best Dance Release
 * Nominated
 * Breakthrough Artist – Album
 * Nominated
 * Breakthrough Artist – Album
 * Nominated
 * Nominated

title: Sonic Animation


text:
Talk:Hahn–Banach theorem

Generalizations and Counter-Examples
In addition to failing in non-convex topological vector spaces for the domain, Hahn-Banach fails for maps into normed vector spaces. It would be nice to point out some results in this direction.

mistake?
In the second important consequence, in the last formula instead of 1/||z|| must be 1/dist(z,U). The same mistake in other languages except for Polish.Dy76 (talk) 13:27, 19 January 2008 (UTC)

if V is a normed vector space with subspace U (not necessarily closed) and if z is an element of V not in the closure of U, then there exists a continuous linear map ψ : V -> K with ψ(x) = 0 for all x in U, ψ(z) = 1, and ||ψ|| = ||z||-1.

I think "not necessarily closed" is wrong here. But can't make up a counterexample right now.
 * What do you mean "wrong" ? It's a hypothesis, it cannot be right or wrong... It could be unnecessary to mention it, but it can't be wrong.
 * Uhm, he means that the assertion is false, when (not necessarily closed) appear where it does. The implication is rendered false.
 * However, it is seems ok as it stands, since z is assumed to be outside the closure of U, and thus have positive distance to U.
 * But, as formulated above it is surely false. There will be small elements close to any subspace, and thus the norm of the functional would be negative... remove the -1 and it seems fine.

AC, Hahn-Banach and Banach-Tarski
Suppose you assume ZF as the axioms of set theory (i.e. without AC or its negation). You also assume the Hahn-Banach theorem is true. Can you prove AC? If yes, I think that means you can't get rid of the Banach-Tarski paradox without also losing the Hahn-Banach theorem. Is that interesting? 70.231.131.185 18:37, 8 February 2006 (UTC)

 * The following implications hold:
 * AC → BPI → "BM" → Hahn-Banach theorem → Banach-Tarski paradox.
 * where "BM" means that on every Boolean algebra there is a finitely additive measure.
 * The first implication is of course well-known, and it is known that the reverse does not hold.
 * The second implication is trivial (take the discrete measure), and I do not know if the reverse holds.
 * I think that the third implication is actually an equivalence, but I am not sure.
 * The fourth implication is proved in a paper by Janusz Pawlikowski in Fund. Math. 138 (1991). (The paper also mentions or perhaps proves the third implication.)
 * So the answer is: No, you cannot prove AC from Hahn-Banach.  But yes, if you get rid of Banach-Tarski, you also lose Hahn-Banach.
 * Aleph4 23:29, 20 April 2006 (UTC)

redirect?
I'd like to rename this page to "Hahn-Banach theorem" (with an ordinary hyphen instead of the Unicode dash) and fix the links and get rid of the redirect. Any reason not to do that? It took a lot of head scratching for me to figure out how "Hahn-Banach theorem" could be redirected here, i.e. that the title of this page is actually something different. 70.231.131.185 05:25, 9 February 2006 (UTC)

 * Please don't do things like that. There is no reason to do it. It's just a time-sink going over this with everyone, but there is a good copy editor's convention that is being followed here. Charles Matthews 21:53, 9 February 2006 (UTC)

 * Blecch. The reason to do it is because the hyphen is much easier to type, is almost always what people type, and is what almost all the internal wikipedia links use, which means that with the en dash in the article title, all those links go to redirects and sometimes double redirects.  The reason not to do it is in WP:MOSDASH which I just found.  Maybe the solution is to adopt a convention of writing a double hyphen for the en dash, like in TeX, and put a code patch into the MediaWiki software to transform the double hyphen into the Unicode symbol, sort of like TeX does.  Triple hyphen would similarly transform to an em dash.  I can work on that patch if it's worthwhile, but I probably won't get a chance to do it real soon (there's other stuff I need to finish first).    It would also have to get wider discussion since it would affect a lot of places where people typed double hyphens to express something like an em dash.  Let me know what you think.  (Actually I see now there's a huge discussion on WP:MOSDASH's talk page about the double hyphen suggestion.  In my not-so-copious free time I'll someday try to get around to finding out what happened with it. Phr 00:41, 11 February 2006 (UTC)

infinite sub-linear function
the sub-linear function defined N:V->R but isn't it possible for it to have infinite values too? --itaj 00:23, 3 May 2006 (UTC)

 * I think that's a valid point. The book I looked at specifically mentions that N must be a finite sub-linear functional, since sub-linear functionals can be infinite-valued. Lavaka 18:30, 22 August 2006 (UTC)

fields
The statement of the H-B theorem says the range of N is the reals, while the range of $$\psi$$ and $$\phi$$ are the scalar field K. This seems odd to me. We require that the extension $$\psi$$ be dominated by N, but how to compare the values of the functions if one is in the reals and the other in K? Earlier, it is mentioned that K is the scalar field (either the reals or complex). This seems sloppy: do we restrict K to just the reals and complex, or was the parenthetical comment just meant as an example, in which case it should use a word like "e.g." or "ex.". If it is restricted to the reals or complex, then we can compare N and K using the absolute value or complex modulus, but this should be made clear. The book I use simplifies everything and assumes K is the reals and doesn't get itself into trouble. --Lavaka 18:48, 22 August 2006 (UTC)

TeXify math?
At least on my computer screen, the mathematical formulae used in the article text are barely readable, and I would like to translate them to TeX, unless anybody disagress. — Tobias Bergemann 11:40, 4 May 2007 (UTC)
 * Translating inline formulas to TeX may cause some of them to become PNGs, and one some screens those look huge. The math style manual kind of discourages that. As long as you attempt to minimize inline PNGs I guess translating to TeX should be fine. By the way, the html formulas look perfect on my own screen. Oleg Alexandrov (talk) 15:28, 4 May 2007 (UTC)

Eduard Helly
The story of Eduard Helly proving Hahn-Banach 20 years before Hahn and Banach seems to be supported by Mac Tutor. I suppose we should add it. -- Tiphareth (talk) 11:45, 19 November 2007 (UTC)

Most general formulation
Isn't the formulation for convex functions as seen in Reed and Simon the most general for R vector spaces? I think this should be added somewhere. Also it should be made clear that the other formulation from Reed and Simon, the last in the section "Formulation" is meant for complex vector spaces. Quiet photon (talk) 18:40, 8 May 2010 (UTC)

Applications
Apart from "Consequences" which are direct corollaries couldn't any non-trivial applications be mentioned? —Preceding unsigned comment added by 78.157.76.143 (talk) 18:33, 23 May 2010 (UTC)

Domination by convex functional
There is a more general formulation of the Hahn-Banach theorem, which is hardly found in any textbooks on functional analysis and only demanded for $$\mathcal{N}$$ to be convex. It is clear that every sublinear function by

$$ \forall x,y \in V \forall \lambda\in [0,1]: f(\lambda x+ (1-\lambda)y) \leq f(\lambda x) + f((1-\lambda)y) = \lambda f(x) +(1-\lambda)f(y) $$

is convex.

Hence the most general formulation of Hahn-Banach in the real case is the following theorem from the paper A Remark Concerning Hahn-Banach's Extension Theorem and the Quasilinearization of Convex Functionals by L. Bittner (1971):  The Hahn–Banach theorem states that if $$\scriptstyle\mathcal{N}:\; V\rightarrow [0,\infty)$$ is a convex functional, and $$\scriptstyle\varphi:\; U\rightarrow\mathbb{R}$$ is a linear functional on a linear subspace U ⊆ V which is dominated by $$\scriptstyle\mathcal{N}$$ on U,

 * $$\varphi(x) \leq \mathcal{N}(x)\qquad\forall x \in U$$

then there exists a linear extension $$\scriptstyle\psi:\; V\rightarrow\mathbb{R}$$ of $$\varphi$$ to the whole space V, i.e., there exists a linear functional ψ such that

 * $$\psi(x)=\varphi(x)\qquad\forall x\in U$$

and

 * $$\psi(x) \le \mathcal{N}(x)\qquad\forall x\in V.$$

But note, that the convex version, indeed need the assumption, that $\mathcal{N}$ is sublinear. Balkenbrenner (talk) 22:02, 8 November 2011 (UTC)

 * I think this is precisely the version of HBT given in Aliprantis-Border: Infinite dimensional analysis, p.195, Theorem 5.53. I tried searching google books for phrases like "hahn-banach theorem" "dominated by a convex" or "hahn-banach theorem" "convex function" and found this book: Foundations of optimization By Osman Güler, Graduate Texts in Mathematics 258 gives both formulations, In Theorem 6.40 on p.167 the dominating functional is sublinear, in Theorem 6.41 on p.168 the dominating functional is convex. I do not have the access to that paper now, but if my notes are correct, the version with convex function appears also in J. D. Weston: A Note on the Extension of Linear Funtionals; The American Mathematical Monthly, Vol. 67, No. 5 (May, 1960), pp. 444-445 . --Kompik (talk) 17:46, 28 December 2011 (UTC)

 * You are right, Weston's result is:

Let g be a convex functional on a real vector space X, let X0 be a vector subspace of X, and let f0 be a linear functional on X0 such that f0(x) < g(x) for all x in Xo. Then there is a linear functional f on X such that f(x) =f0(x) for all x in Xo, and f(x) <g(x) for all x in X
 * If you wish, I can send you Weston's article. Sasha (talk) 20:39, 28 December 2011 (UTC)

 * Sasha there's no need for sending me the article, I'll be able to access jstor when I'm back at my workplace (in a few days). But thanks for the quote. --Kompik (talk) 06:46, 29 December 2011 (UTC)

 * The only assumption required is that the functional is convex. No extra assumptions on the functional (e.g. positivity, positive homogeneity, subadditivity) are not needed. See Eric Schechter, Handbook of Analysis and Its Foundations, Chapter 12, Academic Press, 1996. ISBN 0-12-622760-8. I've made the necessary edit. -- David Pal (talk) 14:43, 26 April 2018 (UTC)

False main result with sublinear functions instead of seminorms
I think the main theorem (the first stated version of the Hahn-Banach theorem) with the bound $$|f| \le p$$, where $$p$$ is a sublinear function, is false. A counterexample: Let $$\mathbb{K} = \mathbb{R}$$, $$X = \mathbb{R}^2$$, $$p(x,y) = |x|-x+|y|-y$$, $$M = \mathbb{R}(1,-1)$$, $$f(x,-x) = 2x$$. Then $$p$$ is a nonnegative sublinear function (but it is not a seminorm), and $$|f| = p$$ on $$M$$, however there is no linear extension $$F$$ of $$f$$ to $$X$$ such that $$|F| \le p$$, because $$p(1,0) = p(0,1) = 0$$, so $$F$$ would have to be constant $$0$$, but $$f \neq 0$$.

The theorem is true if $$p$$ is a seminorm, see Theorem 3.3 in Rudin. The theorem is also true for sublinear $$p$$, if we omit the absolute values, so we use $$f \le p$$ on $$M$$ and $$F \le p$$ on $$V$$, see Theorem 3.2 in Rudin. 188.36.117.186 (talk) 17:05, 23 June 2021 (UTC)

Problematic PDE section
The subsection "Partial differential equations" needs, at the least, a reference. Moreover it seems to me that it has some content problems. It is not correct that the adjoint of a linear operator is defined only on the image of the operator. And it does not seem to make sense that a standard solution ($u$) is being extended by Hahn-Banach to a weak solution; it is already a standard solution and hence is itself a weak solution by any reasonable definition. Gumshoe2 (talk) 17:35, 8 September 2022 (UTC)

"Mazur's theorem" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Mazur%27s_theorem&redirect=no Mazur's theorem] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. Jay 💬 13:15, 13 February 2024 (UTC)

title: Talk:Hahn–Banach theorem


text:
Soyuz 20

Soyuz 20 (Союз 20, Union 20) was an uncrewed spacecraft launched by the Soviet Union. It was a long-duration test of the Soyuz spacecraft that docked with the Salyut 4 space station. Soyuz 20 performed comprehensive checking of improved on-board systems of the spacecraft under various flight conditions. It also carried a biological payload. Living organisms were exposed to three months in space.

Mission parameters

 * Mass: 6570 kg
 * Perigee: 199.7 km
 * Apogee: 263.5 km
 * Inclination: 51.6°
 * Period: 88.8 minutes

Return
It was recovered on 16 February 1976 at 02:24 UTC.

title: Soyuz 20


text:
Under the Running Board

Under the Running Board is an EP by American mathcore band the Dillinger Escape Plan, released on October 22, 1998. The album shows a more experimental side, which would later be more developed on Calculating Infinity. This is also the band's first release on Relapse Records. The song "Abe the Cop" would later be performed and recorded on their self-titled EP's re-release in 2000.

Reissue
Almost 10 years to the day of its original release, Under the Running Board was re-released by Relapse Records. The reissue contains the original three tracks plus 10 bonus tracks.

Personnel

 * Adam Doll – bass
 * Dimitri Minakakis – vocals
 * Chris Pennie – drums
 * Ben Weinman – lead guitar, vocals
 * John Fulton – rhythm guitar
 * Liam Wilson - bass (reissue bonus tracks)
 * Brian Benoit - rhythm guitar (reissue bonus tracks 4-12)

Additional personnel

 * Alan Douches – mastering
 * Steve Evetts – producer, engineer
 * Adam Peterson – graphic design

title: Under the Running Board


text:
Allenton

Allenton may refer to:

Places

 * Allenton, Derbyshire, England
 * Allenton, New Zealand, a suburb in the town of Ashburton, New Zealand
 * Allenton, Northumberland, England is now called Alwinton
 * Allenton, Michigan, USA
 * Allenton, Wisconsin, USA

title: Allenton


text: Category:Images with unknown source

title: Category:Images with unknown source


text:
Egon Eiermann

Egon Eiermann (29 September 1904 – 19 July 1970 ) was one of Germany's most prominent architects in the second half of the 20th century. He was also a furniture designer. From 1947, he was Professor for architecture at Technische Hochschule Karlsruhe (today Karlsruhe Institute of Technology).

Biography
Eiermann was born in Neuendorf bei Potsdam (now part of Babelsberg, Potsdam), the son of Wilhelm Eiermann (1874–1948), a locomotive engineer and his wife Emma Gellhorn (1875–1959). He archived his Abitur at the Althoff-Gymnasium and studied architecture at Technische Universität Berlin. From 1925 to 1928, he was master student of Hans Poelzig. After graduating in 1928, he gained professional experience in the construction departments of Karstadt AG in Hamburg and the Berlin electricity works (Bewag (Berlin)). From 1931 to 1945, he was an independent architect in Berlin and initially planned residential buildings. Before World War II he had an office with fellow architect Fritz Jaenecke. During the Nazi era, he mainly created industrial architecture. In 1945, he escaped to Buchen in West Germany, the birthplace of the father. From 1946 to 1965, he had a shared office with Robert Hilgers. In 1948, the office was relocated to Karlsruhe. He joined the faculty of the Technische Hochschule Karlsruhe in 1947, working there on developing steel frame construction methods. Students were Oswald Mathias Ungers and Julia Bolles-Wilson. During a study trip to the United States in 1950, he met Walter Gropius, Marcel Breuer and Konrad Wachsmann in Boston, and in 1956 also Ludwig Mies van der Rohe. In 1967, Eiermann chaired the jury in the architectural competition for the Olympic Park in Munich.

Personal life
In 1940, he married in Berlin interior designer Charlotte, Friedheim (1912–2001) and in 1954 in Berlin architect Brigitte, née Feyerabendt (1924–2019). He had two children: with his first wife Andreas (born 1942), from his second marriage Anna (born 1956).

He died in Baden-Baden, aged 65. He is buried at the Buchen Cemetery.

Works
During the years of reconstruction, his steel-frame industrial buildings became exemplary. The buildings are transparent, inviting, democratic, making order visible.

A functionalist, his major works include: the textile mill at Blumberg (1951); the West German pavilion at the Brussels World's Fair (with Sep Ruf, 1958); the Embassy of Germany, Washington, D.C. (1958–1964); the highrise Langer Eugen for the German Parliament in Bonn (1965–1969); the IBM-Germany Headquarters in Stuttgart (1967–1972); and, the Olivetti building in Frankfurt (1968–1972). By far his most famous work is the new church on the site of the Kaiser Wilhelm Memorial Church in Berlin (1959–1963).

The sets of the 1926 film The Pink Diamond were designed by Eiermann.

Source:

 * 1929–1930 Substation of the Berliner Elektrizitätswerke AG, Berlin-Steglitz
 * 1931–1933 Hesse residential building, Berlin-Lankwitz
 * 1936–1937 Steingroever residential building, Berlin-Grunewald
 * 1938 factory building and boiler house of the Degea-AG-Auergesellschaft, Berlin-Wedding
 * 1938–1939 expansion and conversion of the Total-Werke Foerstner & Co, Apolda
 * 1939–1941 factory buildings of Märkische Metallbau GmbH, Oranienburg
 * 1948–1950 administration and factory building of Ciba AG, Wehr/Baden
 * 1949–1950 handkerchief weaving mill/spinning mill, Blumberg/Black Forest
 * 1950–1953 administration building of the United Silk Weaving Works, Krefeld
 * 1951–1956 experimental power plant of TU Karlsruhe
 * 1953 St. Matthew Church, Pforzheim
 * 1953–1954 Burda Moden publishing house, Offenburg
 * 1954–1961 residential building, Interbau, Hansaviertel, Berlin-Tiergarten
 * 1955–1957 Volkshilfe administration building, Cologne
 * 1956–1958 German Pavilion, World Exhibition in Brussels (with Sep Ruf, exterior planning by Walter Rossow)
 * 1956–1960 administration building of Steinkohlebergwerke AG, Essen
 * 1957–1963 Kaiser Wilhelm Memorial Church, Berlin-Charlottenburg
 * 1958–1961 Head office of Neckermann Versand KG, Frankfurt am Main
 * 1958–1961 administration building of the steel structure Gustav Müller, Offenburg
 * 1958–1964 Chancellery building of the German Embassy, Washington
 * 1959–1962 Eiermann house, Baden-Baden
 * 1961–1967 buildings for the DEA-Scholven GmbH refinery, Karlsruhe
 * 1965–1969 high-rise building for members of the German Bundestag, Bonn
 * 1967–1972 Administration and training center of Deutsche Olivetti, Frankfurt am Main,
 * 1967–1972 IBM headquarters, Stuttgart-Vaihingen (Eiermann-Campus)

Design
From 1949, the first functional and serially produced seating furniture made of wood and tubular steel was created in cooperation with the Esslingen company Wilde + Spieth.

Source:

 * 1950 SE 68 tubular steel chair
 * 1952 E 10 wicker chair
 * 1952–1953 SE 18 wooden folding chair
 * 1953 table frame Eiermann 1
 * 1960–1961 Church seat SE 121
 * 1965 table frame Eiermann 2

Awards
Source:

 * 1962 Berlin Art Prize
 * 1965 honorary doctorate from Technische Universität Berlin
 * 1965 Grand State Prize for Architecture of the State of North Rhine-Westphalia
 * 1968 Grand Prize of the Association of German Architects (Großer BDA Preis)
 * 1968 Grand Federal Cross of Merit
 * 1969 Hugo Häring Prize of the BDA Baden-Württemberg
 * 1970 Order Pour le Mérite for Science and Arts

In 1997, the Egon Eiermann Society was founded in Karlsruhe. In 2004, the Bundespost honored Eiermann with a special postage stamp. In Karlsruhe, Egon-Eiermann-Allee (49.03677°N, 8.34895°W) was named after him in 2009. One of the lecture halls in the architectural building (49.01115°N, 8.41107°W) of the Karlsruhe Institute of Technology bears his name. The Egon Eiermann Award is an international ideas competition in architecture.

Memberships
Source:
 * 1926 Founding member of the "Group of Young Architects" ("Gruppe junger Architekten")
 * 1931 Member of the Association of German Architects (Bund Deutscher Architekten)
 * 1931 Member of Deutscher Werkbund
 * 1951 Founding member of the German Design Council (Rat für Formgebung)
 * 1955 Member of the Academy of Arts, Berlin (West), Section Architecture
 * 1960 Honorary member of the Central Association of Austrian Architects
 * 1962 Member of the planning council for the new buildings of the German Bundestag and the German Bundesrat in Bonn
 * 1963 Corresponding Honorary Member of the Royal Institute of British Architects
 * 1969 Founding member of the Housing and Environment Institute of the Hessian state government

title: Egon Eiermann


text:
Faustus Cornelius Sulla Felix

Faustus Cornelius Sulla Felix (22 – 62 AD) was one of the lesser known figures of the Julio-Claudian dynasty of Ancient Rome.

Life
Felix was the son of Domitia Lepida the Younger and the suffect consul of 31, Faustus Cornelius Sulla Lucullus, a descendant of the Dictator Lucius Cornelius Sulla. His maternal grandparents were Antonia Major and Lucius Domitius Ahenobarbus. His maternal grandmother Antonia Major was a niece of the emperor Augustus and his mother, Domitia Lepida, was a great-niece of Augustus, being a granddaughter of Augustus’ sister Octavia the Younger and the triumvir Mark Antony. Felix was a maternal younger half-brother of the empress Valeria Messalina.

In 47 the emperor Claudius, who was his mother's cousin, arranged for Felix to marry his daughter, Claudia Antonia. Antonia bore Felix a son, who was reportedly frail and died before his second birthday. The boy's first birthday was celebrated privately. Felix's attachment to the imperial family brought him an early consulship in 52.

In 55, the year after the accession of the emperor Nero, the imperial freedman Pallas and the Praetorian prefect Sextus Afranius Burrus were accused of conspiring to have Felix declared emperor. The conspirators were put on trial, but Felix does not appear to have been implicated. Nero, however, began to watch his brother-in-law closely, afraid of his connection to the imperial family.

In 58 another imperial freedman falsely accused Felix of plotting to attack Nero, possibly at the latter's instigation. Nero treated Felix as proven guilty, had him exiled in 59 and confined to Massilia (modern Marseille, France). Finally in 62, the palace guardsman Tigellinus sent assassins to kill Felix. Felix was murdered at dinner, five days after Tigellinus gave his orders, and his head transported to the palace. At times, Nero would tease his head, due to his baldness and greyness of his hair. The historian Tacitus described Felix's character as "timid and despicable" and also stated that Felix was incapable of plotting against Nero.

Now a widow, Claudia Antonia was sought as a wife by Nero, after the death of his second wife, the Empress Poppaea Sabina. When Claudia Antonia refused, Nero had her charged with attempted rebellion and executed her.

title: Faustus Cornelius Sulla Felix


text: Category:Images with unknown copyright status


text:
1937 South American Championship

The fourteenth edition of the South American Championship of football was held in Buenos Aires, Argentina from 27 December 1936 to 1 February 1937.

The participating countries were Argentina, Brazil, Chile, Paraguay, Peru, and Uruguay thus making this the first edition in which more than five teams took part of the event.

Bolivia, and Colombia (a new CONMEBOL member) withdrew from the tournament.

Because of the summer heat, most of the matches were played at night, with Estadio Gasómetro being one of the few stadiums in Argentina with artificial lighting at the time, while other games were played during daytime at Estadio Alvear y Tagle.

Squads
For a complete list of participants squads see: 1937 South American Championship squads

Final round
Each team played against each of the other teams. Two points were awarded for a win, one point for a draw and zero points for a defeat.

As Brazil and Argentina finished tied in points, a playoff was required to determine the champion.

Goal scorers
7 goals 5 goals
 * Raúl Toro

 * 🇦🇷 Alberto Zozaya
 * Severino Varela

4 goals

 * 🇧🇷 Luisinho
 * 🇧🇷 Patesko

3 goals

 * 🇦🇷 Francisco Varallo
 * 🇧🇷 Carvalho Leite
 * Juan Píriz

2 goals

 * 🇦🇷 Vicente de la Mata
 * 🇦🇷 Enrique García
 * 🇦🇷 Alejandro Scopelli
 * 🇧🇷 Niginho
 * 🇧🇷 Roberto
 * Aurelio González
 * Amadeo Ortega
 * 🇵🇪 Teodoro Fernández
 * 🇵🇪 Jorge Alcalde

1 goal

 * 🇧🇷 Afonsinho
 * 🇧🇷 Bahia
 * Manuel Arancibia
 * José Avendaño
 * Arturo Carmona
 * Guillermo Riveros
 * Guillermo Torres
 * Juan Amarilla
 * Adolfo Erico
 * Martín Flor
 * Raúl Núñez Velloso
 * 🇵🇪 Alejandro Villanueva
 * 🇵🇪 Adolfo Magallanes
 * 🇵🇪 Jose Maria Lavalle
 * Adelaido Camaiti
 * Eduardo Ithurbide
 * Segundo Villadóniga

title: 1937 South American Championship


text: User talk:128.125.52.183

title: User talk:128.125.52.183


text: File:Dillinger Escape Plan 'Under the Running Board' album cover.jpg


text: Category:Fair use images

title: Category:Fair use images