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John Robert Schrieffer

John Robert Schrieffer (May 31, 1931 – July 27, 2019) was an American physicist who, with John Bardeen and Leon Cooper, was a recipient of the 1972 Nobel Prize in Physics for developing the BCS theory, the first successful quantum theory of superconductivity.

Life and career
Schrieffer was born in Oak Park, Illinois, the son of Louise (Anderson) and John Henry Schrieffer. His family moved in 1940 to Manhasset, New York, and then in 1947 to Eustis, Florida, where his father, a former pharmaceutical salesman, began a career in the citrus industry. In his Florida days, Schrieffer enjoyed playing with homemade rockets and ham radio, a hobby that sparked an interest in electrical engineering.

After graduating from Eustis High School in 1949, Schrieffer was admitted to the Massachusetts Institute of Technology, where for two years he majored in electrical engineering before switching to physics in his junior year. He completed a bachelor's thesis on multiplets in heavy atoms under the direction of John C. Slater in 1953. Pursuing an interest in solid-state physics, Schrieffer began graduate studies at the University of Illinois at Urbana–Champaign, where he was hired immediately as a research assistant to Bardeen. After working out a theoretical problem of electrical conduction on semiconductor surfaces, Schrieffer spent a year in the laboratory, applying the theory to several surface problems. In his third year of graduate studies, he joined Bardeen and Cooper in developing the theory of superconductivity.

Schrieffer recalled that in January 1957 he was on a subway in New York City when he had an idea of how to describe mathematically the ground state of superconducting electrons. Schrieffer and Bardeen's collaborator Cooper had discovered that electrons in a superconductor are grouped in pairs, now called Cooper pairs, and that the motions of all Cooper pairs within a single superconductor are correlated and function as a single entity due to phonon-electron interactions. Schrieffer's mathematical breakthrough was to describe the behavior of all Cooper pairs at the same time, instead of each individual pair. The day after returning to Illinois, Schrieffer showed his equations to Bardeen, who immediately realized they were the solution to the problem. The BCS theory (Bardeen-Cooper-Schrieffer) of superconductivity, as it is now known, accounted for more than 30 years of experimental results that had stymied some of the greatest theorists in physics.

After completing his doctoral dissertation on the theory of superconductivity, Schrieffer spent the 1957–1958 academic year as a National Science Foundation fellow at the University of Birmingham in England and at the Niels Bohr Institute in Copenhagen, where he continued research into superconductivity. Following a year as assistant professor at the University of Chicago, he returned to the University of Illinois in 1959 as a faculty member. In 1960, he went back to the Bohr Institute for a summer visit, during which he became engaged to Anne Grete Thomsen whom he married at Christmas of that year. Two years later, Schrieffer joined the faculty of the University of Pennsylvania in Philadelphia, and, in 1964, Schrieffer published his book on the BCS theory, Theory of Superconductivity. He held honorary degrees from the Technical University of Munich and the University of Geneva. In 1968 Schrieffer, along with Cooper, were awarded the Comstock Prize in Physics from the National Academy of Sciences. He was awarded the Oliver E. Buckley Condensed Matter Prize by the American Physical Society the same year.

Schrieffer was elected to the American Academy of Arts and Sciences in 1970 and the United States National Academy of Sciences in 1971. In 1972, he, along with Bardeen and Cooper, won the 1972 Nobel Prize in Physics for developing the BCS theory. Schrieffer was elected to the American Philosophical Society in 1975. In 1980, Schrieffer became a professor at the University of California, Santa Barbara, and rose to chancellor professor in 1984, serving as director of the university's Kavli Institute for Theoretical Physics. In 1992, Florida State University appointed Schrieffer as a university eminent scholar professor and chief scientist of the National High Magnetic Field Laboratory, where he continued to pursue one of the great goals in physics: room temperature superconductivity.

On September 24, 2004, while driving with a suspended license, Schrieffer was involved in an automobile accident that killed one person and injured seven others. Schrieffer was said to have fallen asleep at the wheel of his car. On November 6, 2005, he was sentenced to two years in prison for vehicular manslaughter. Schrieffer was incarcerated in Richard J. Donovan Correctional Facility at Rock Mountain near San Diego, California.

He died in late July 2019 at a nursing facility in Florida while sleeping. He was 88 years old.

title: John Robert Schrieffer


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Californian

Californian is an adjective describing something related to the American state of California. It is also the demonym for a person from California.

It may also refer to:

Ships

 * Californian (schooner), the "Official Tall Ship Ambassador for the State of California"
 * Californian (ship)
 * SS Californian, British passenger ship famous for her relationship to the RMS Titanic disaster of 1912
 * MV Californian (1921), early American motor vessel

Other uses

 * Californian, a font designed by Frederic Goudy for the University of California Press
 * The Californian, a coupe version of the British Hillman Imp automobile
 * The Salinas Californian, the daily newspaper of Salinas, California
 * The Bakersfield Californian, the daily newspaper of Bakersfield, California

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

title: Californian


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Descriptive set theory

In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the study of operator algebras and group actions, and mathematical logic.

Polish spaces
Descriptive set theory begins with the study of Polish spaces and their Borel sets.

A Polish space is a second-countable topological space that is metrizable with a complete metric. Heuristically, it is a complete separable metric space whose metric has been "forgotten". Examples include the real line $$\mathbb{R}$$, the Baire space $$\mathcal{N}$$, the Cantor space $$\mathcal{C}$$, and the Hilbert cube $$I^{\mathbb{N}}$$.

Universality properties
The class of Polish spaces has several universality properties, which show that there is no loss of generality in considering Polish spaces of certain restricted forms.

 * Every Polish space is homeomorphic to a Gδ subspace of the Hilbert cube, and every Gδ subspace of the Hilbert cube is Polish.
 * Every Polish space is obtained as a continuous image of Baire space; in fact every Polish space is the image of a continuous bijection defined on a closed subset of Baire space. Similarly, every compact Polish space is a continuous image of Cantor space.

Because of these universality properties, and because the Baire space $$\mathcal{N}$$ has the convenient property that it is homeomorphic to $$\mathcal{N}^\omega$$, many results in descriptive set theory are proved in the context of Baire space alone.

Borel sets
The class of Borel sets of a topological space X consists of all sets in the smallest σ-algebra containing the open sets of X. This means that the Borel sets of X are the smallest collection of sets such that:
 * Every open subset of X is a Borel set.
 * If A is a Borel set, so is $$X \setminus A$$. That is, the class of Borel sets are closed under complementation.
 * If An is a Borel set for each natural number n, then the union $$\bigcup A_n$$ is a Borel set. That is, the Borel sets are closed under countable unions.

A fundamental result shows that any two uncountable Polish spaces X and Y are Borel isomorphic: there is a bijection from X to Y such that the preimage of any Borel set is Borel, and the image of any Borel set is Borel. This gives additional justification to the practice of restricting attention to Baire space and Cantor space, since these and any other Polish spaces are all isomorphic at the level of Borel sets.

Borel hierarchy
Each Borel set of a Polish space is classified in the Borel hierarchy based on how many times the operations of countable union and complementation must be used to obtain the set, beginning from open sets. The classification is in terms of countable ordinal numbers. For each nonzero countable ordinal α there are classes $$\mathbf{\Sigma}^0_\alpha$$, $$\mathbf{\Pi}^0_\alpha$$, and $$\mathbf{\Delta}^0_\alpha$$.
 * Every open set is declared to be $$\mathbf{\Sigma}^0_1$$.
 * A set is declared to be $$\mathbf{\Pi}^0_\alpha$$ if and only if its complement is $$\mathbf{\Sigma}^0_\alpha$$.
 * A set A is declared to be $$\mathbf{\Sigma}^0_\delta$$, δ > 1, if there is a sequence ⟨ Ai ⟩ of sets, each of which is $$\mathbf{\Pi}^0_{\lambda(i)}$$ for some λ(i) < δ, such that $$A = \bigcup A_i$$.
 * A set is $$\mathbf{\Delta}^0_\alpha$$ if and only if it is both $$\mathbf{\Sigma}^0_\alpha$$ and $$\mathbf{\Pi}^0_\alpha$$.

A theorem shows that any set that is $$\mathbf{\Sigma}^0_\alpha$$ or $$\mathbf{\Pi}^0_\alpha$$ is $$\mathbf{\Delta}^0_{\alpha + 1}$$, and any $$\mathbf{\Delta}^0_\beta$$ set is both $$\mathbf{\Sigma}^0_\alpha$$ and $$\mathbf{\Pi}^0_\alpha$$ for all α > β. Thus the hierarchy has the following structure, where arrows indicate inclusion.

$ \begin{matrix} & & \mathbf{\Sigma}^0_1 & & & & \mathbf{\Sigma}^0_2 & & \cdots \\ & \nearrow & & \searrow & & \nearrow \\ \mathbf{\Delta}^0_1 & & & & \mathbf{\Delta}^0_2 & & & & \cdots \\ & \searrow & & \nearrow & & \searrow \\ & & \mathbf{\Pi}^0_1 & & & & \mathbf{\Pi}^0_2 & & \cdots \end{matrix}\begin{matrix} & & \mathbf{\Sigma}^0_\alpha & & & \cdots \\ & \nearrow & & \searrow \\ \quad \mathbf{\Delta}^0_\alpha & & & & \mathbf{\Delta}^0_{\alpha + 1} & \cdots \\ & \searrow & & \nearrow \\ & & \mathbf{\Pi}^0_\alpha & & & \cdots \end{matrix} $

Regularity properties of Borel sets
Classical descriptive set theory includes the study of regularity properties of Borel sets. For example, all Borel sets of a Polish space have the property of Baire and the perfect set property. Modern descriptive set theory includes the study of the ways in which these results generalize, or fail to generalize, to other classes of subsets of Polish spaces.

Analytic and coanalytic sets
Just beyond the Borel sets in complexity are the analytic sets and coanalytic sets. A subset of a Polish space X is analytic if it is the continuous image of a Borel subset of some other Polish space. Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets. A set is coanalytic if its complement is analytic.

Projective sets and Wadge degrees
Many questions in descriptive set theory ultimately depend upon set-theoretic considerations and the properties of ordinal and cardinal numbers. This phenomenon is particularly apparent in the projective sets. These are defined via the projective hierarchy on a Polish space X:
 * A set is declared to be $$\mathbf{\Sigma}^1_1$$ if it is analytic.
 * A set is $$\mathbf{\Pi}^1_1$$ if it is coanalytic.
 * A set A is $$\mathbf{\Sigma}^1_{n+1}$$ if there is a $$\mathbf{\Pi}^1_n$$ subset B of $$X \times X$$ such that A is the projection of B to the first coordinate.
 * A set A is $$\mathbf{\Pi}^1_{n+1}$$ if there is a $$\mathbf{\Sigma}^1_n$$ subset B of $$X \times X$$ such that A is the projection of B to the first coordinate.
 * A set is $$\mathbf{\Delta}^1_{n}$$ if it is both $$\mathbf{\Pi}^1_n$$ and $$\mathbf{\Sigma}^1_n$$.

As with the Borel hierarchy, for each n, any $$\mathbf{\Delta}^1_n$$ set is both $$\mathbf{\Sigma}^1_{n+1}$$ and $$\mathbf{\Pi}^1_{n+1}$$.

The properties of the projective sets are not completely determined by ZFC. Under the assumption V = L, not all projective sets have the perfect set property or the property of Baire. However, under the assumption of projective determinacy, all projective sets have both the perfect set property and the property of Baire. This is related to the fact that ZFC proves Borel determinacy, but not projective determinacy.

There are also generic extensions of $$L$$ for any natural number $$n>2$$ in which $$\mathcal P(\omega)\cap L$$ consists of all the lightface $$\Delta^1_n$$ subsets of $$\omega$$.

More generally, the entire collection of sets of elements of a Polish space X can be grouped into equivalence classes, known as Wadge degrees, that generalize the projective hierarchy. These degrees are ordered in the Wadge hierarchy. The axiom of determinacy implies that the Wadge hierarchy on any Polish space is well-founded and of length Θ, with structure extending the projective hierarchy.

Borel equivalence relations
A contemporary area of research in descriptive set theory studies Borel equivalence relations. A Borel equivalence relation on a Polish space X is a Borel subset of $$X \times X$$ that is an equivalence relation on X.

Effective descriptive set theory
The area of effective descriptive set theory combines the methods of descriptive set theory with those of generalized recursion theory (especially hyperarithmetical theory). In particular, it focuses on lightface analogues of hierarchies of classical descriptive set theory. Thus the hyperarithmetic hierarchy is studied instead of the Borel hierarchy, and the analytical hierarchy instead of the projective hierarchy. This research is related to weaker versions of set theory such as Kripke–Platek set theory and second-order arithmetic.

title: Descriptive set theory


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Ivar Giaever

Ivar Giaever (Giæver, ; born April 5, 1929) is a Norwegian-American engineer and physicist who shared the Nobel Prize in Physics in 1973 with Leo Esaki and Brian Josephson "for their discoveries regarding tunnelling phenomena in solids". Giaever's share of the prize was specifically for his "experimental discoveries regarding tunnelling phenomena in superconductors".

In 1975, he was elected as a member into the National Academy of Engineering for contributions in the discovery and elaboration of electron tunneling into superconductors.

Giaever is a professor emeritus at the Rensselaer Polytechnic Institute and the president of the company Applied Biophysics.

Early life and education
Giaever earned a degree in mechanical engineering from the Norwegian Institute of Technology in Trondheim in 1952. In 1954, he emigrated from Norway to Canada, where he was employed by the Canadian division of General Electric. He moved to the United States four years later, joining General Electric's Corporate Research and Development Center in Schenectady, New York, in 1958. He has lived in Niskayuna, New York, since then, taking up US citizenship in 1964. While working for General Electric, Giaever earned a Ph.D. degree at the Rensselaer Polytechnic Institute in 1964.

The Nobel Prize
The work that led to Giaever's Nobel Prize was performed at General Electric in 1960. Following on Esaki's discovery of electron tunnelling in semiconductors in 1958, Giaever showed that tunnelling also took place in superconductors, demonstrating tunnelling through a very thin layer of oxide surrounded on both sides by metal in a superconducting or normal state. Giaever's experiments demonstrated the existence of an energy gap in superconductors, one of the most important predictions of the BCS theory of superconductivity, which had been developed in 1957. Giaever's experimental demonstration of tunnelling in superconductors stimulated the theoretical physicist Brian Josephson to work on the phenomenon, leading to his prediction of the Josephson effect in 1962. Esaki and Giaever shared half of the 1973 Nobel Prize, and Josephson received the other half.

Giaever's research later in his career was mainly in the field of biophysics. In 1969, he researched biophysics for a year as a fellow at Clare Hall, University of Cambridge, through a Guggenheim Fellowship, and he continued to work in this area after he returned to the US.

He has co-signed a letter from over 70 Nobel laureate scientists to the Louisiana Legislature supporting the repeal of Louisiana’s Louisiana Science Education Act.

Other prizes
In addition to the Nobel Prize, he has also been awarded the Oliver E. Buckley Prize by the American Physical Society in 1965, the Golden Plate Award of the American Academy of Achievement in 1966, and the Zworykin Award by the National Academy of Engineering in 1975.

In 1985, he was awarded an honorary degree, doctor honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology.

He is a member of the Norwegian Academy of Science and Letters.

Global warming
Giaever has repeatedly professed skepticism of global warming, calling it a "new religion". On 13 September 2011, he resigned from the American Physical Society over its official position.

Giaever is currently a science advisor with American conservative and libertarian think tank The Heartland Institute.

Personal life
Giaever was married to his childhood sweetheart Inger (née Skramstad) from 1952 until her death on September 12, 2023 at the age of 94. They have four children: John, Anne, Guri and Trine.

Giaever is an atheist.

Selected publications

 * Giaever, Ivar (2016). "I Am The Smartest Man I Know": A Nobel Laureate's Difficult Journey, World Scientific. ISBN 978-981-3109-17-9.
 * Giaever, Ivar (2016). "I Am The Smartest Man I Know": A Nobel Laureate's Difficult Journey, World Scientific. ISBN 978-981-3109-17-9.
 * Giaever, Ivar (2016). "I Am The Smartest Man I Know": A Nobel Laureate's Difficult Journey, World Scientific. ISBN 978-981-3109-17-9.
 * Giaever, Ivar (2016). "I Am The Smartest Man I Know": A Nobel Laureate's Difficult Journey, World Scientific. ISBN 978-981-3109-17-9.

title: Ivar Giaever


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Polish space

In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations. Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory.

Common examples of Polish spaces are the real line, any separable Banach space, the Cantor space, and the Baire space. Additionally, some spaces that are not complete metric spaces in the usual metric may be Polish; e.g., the open interval $(0, 1)$ is Polish.

Between any two uncountable Polish spaces, there is a Borel isomorphism; that is, a bijection that preserves the Borel structure. In particular, every uncountable Polish space has the cardinality of the continuum.

Lusin spaces, Suslin spaces, and Radon spaces are generalizations of Polish spaces.

Properties

 * 1) Every Polish space is second countable (by virtue of being separable and metrizable).
 * 2) A subspace $Q$ of a Polish space $P$ is Polish (under the induced topology) if and only if $Q$ is the intersection of a sequence of open subsets of $P$.
 * 3) (Cantor–Bendixson theorem) If $X$ is Polish then any closed subset of $X$ can be written as the disjoint union of a perfect set and a countable set. Further, if the Polish space $X$ is uncountable, it can be written as the disjoint union of a perfect set and a countable open set.
 * 4) Every Polish space is homeomorphic to a $G_{δ}$-subset of the Hilbert cube (that is, of $I$, where $I$ is the unit interval and $N$ is the set of natural numbers).

The following spaces are Polish:
 * closed subsets of a Polish space,
 * open subsets of a Polish space,
 * products and disjoint unions of countable families of Polish spaces,
 * locally compact spaces that are metrizable and countable at infinity,
 * countable intersections of Polish subspaces of a Hausdorff topological space,
 * the set of irrational numbers with the topology induced by the standard topology of the real line.

Characterization
There are numerous characterizations that tell when a second-countable topological space is metrizable, such as Urysohn's metrization theorem. The problem of determining whether a metrizable space is completely metrizable is more difficult. Topological spaces such as the open unit interval (0,1) can be given both complete metrics and incomplete metrics generating their topology.

There is a characterization of complete separable metric spaces in terms of a game known as the strong Choquet game. A separable metric space is completely metrizable if and only if the second player has a winning strategy in this game.

A second characterization follows from Alexandrov's theorem. It states that a separable metric space is completely metrizable if and only if it is a $$G_\delta$$ subset of its completion in the original metric.

Polish metric spaces
Although Polish spaces are metrizable, they are not in and of themselves metric spaces; each Polish space admits many complete metrics giving rise to the same topology, but no one of these is singled out or distinguished. A Polish space with a distinguished complete metric is called a Polish metric space. An alternative approach, equivalent to the one given here, is first to define "Polish metric space" to mean "complete separable metric space", and then to define a "Polish space" as the topological space obtained from a Polish metric space by forgetting the metric.

Lusin spaces
A Hausdorff topological space is a Lusin space (named after Nikolai Lusin) if some stronger topology makes it into a Polish space.

There are many ways to form Lusin spaces. In particular:
 * Every Polish space is a Lusin space
 * A subspace of a Lusin space is a Lusin space if and only if it is a Borel set.
 * Any countable union or intersection of Lusin subspaces of a Hausdorff space is a Lusin space.
 * The product of a countable number of Lusin spaces is a Lusin space.
 * The disjoint union of a countable number of Lusin spaces is a Lusin space.

Suslin spaces
A Hausdorff topological space is a Suslin space (named after Mikhail Suslin) if it is the image of a Polish space under a continuous mapping. So every Lusin space is Suslin. In a Polish space, a subset is a Suslin space if and only if it is a Suslin set (an image of the Suslin operation).

The following are Suslin spaces:
 * closed or open subsets of a Suslin space,
 * countable products and disjoint unions of Suslin spaces,
 * countable intersections or countable unions of Suslin subspaces of a Hausdorff topological space,
 * continuous images of Suslin spaces,
 * Borel subsets of a Suslin space.

They have the following properties:
 * Every Suslin space is separable.

Radon spaces
A Radon space, named after Johann Radon, is a topological space on which every Borel probability measure on $M$ is inner regular. Since a probability measure is globally finite, and hence a locally finite measure, every probability measure on a Radon space is also a Radon measure. In particular a separable complete metric space $(M, d)$ is a Radon space.

Every Suslin space is a Radon space.

Polish groups
A Polish group is a topological group $G$ that is also a Polish space, in other words homeomorphic to a separable complete metric space. There are several classic results of Banach, Freudenthal and Kuratowski on homomorphisms between Polish groups. Firstly, Banach's argument applies mutatis mutandis to non-Abelian Polish groups: if $G$ and $H$ are separable metric spaces with $G$ Polish, then any Borel homomorphism from $G$ to $H$ is continuous. Secondly, there is a version of the open mapping theorem or the closed graph theorem due to Kuratowski: a continuous injective homomorphism of a Polish subgroup $G$ onto another Polish group $H$ is an open mapping. As a result, it is a remarkable fact about Polish groups that Baire-measurable mappings (i.e., for which the preimage of any open set has the property of Baire) that are homomorphisms between them are automatically continuous. The group of homeomorphisms of the Hilbert cube $[0,1]^{N}$ is a universal Polish group, in the sense that every Polish group is isomorphic to a closed subgroup of it.

Examples:
 * All finite dimensional Lie groups with a countable number of components are Polish groups.
 * The unitary group of a separable Hilbert space (with the strong operator topology) is a Polish group.
 * The group of homeomorphisms of a compact metric space is a Polish group.
 * The product of a countable number of Polish groups is a Polish group.
 * The group of isometries of a separable complete metric space is a Polish group

title: Polish space


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Talk:Lusatian Neisse

Untitled
What language is "Lusatian Nysa" supposed to be? It doesn't get any hits at all on Google. --Zundark

The river is known in English as the Neisse, but this is of course unacceptable because it is also the German name, and thus gets entangled in the German-Polish Silesia debate. Adam 04:41, 11 Dec 2003 (UTC)

 * This article should be moved to either Nysa or Neisse since it's the Nysa/Neisse from the Oder-Neisse/Odra-Nysa line. Other rivers of that name are much shorter and less well-known. [[User:Halibutt|Halibutt]] 10:47, Sep 8, 2004 (UTC)

 * I don't think that's terribly important. If you search "Nysa," you get a disambiguation page.  If you search "Neisse," you get this page, but there is a link to the disambiguation page, for other rivers of the same name.  A few weeks ago, I did travel there; I visited Görlitz and Zgorzelec, both.  It did strike me that locally there, on maps and such they do generally give the full name of the river--whether in German or in Polish. 140.147.160.78 17:59, 28 June 2007 (UTC)Stephen Kosciesza

Nysa Luzycka
The river does not have the name in English. According to Googlewar the current German name is much less popular than the Polish one, therefore I'm going to rename the article. --Lysy (talk) 17:51, 31 July 2005 (UTC)

Why Lusatian?
It seems that only the Czech, German and Polish names for this river contains the word "Lusatian", simply because Lusatia is near that river? I'm not questioning about the name of the article. I'm just curious about the naming convention.--Fitzwilliam 10:58, 13 July 2006 (UTC)

Its called the Lusatian Neisse because there is another Neisse river to the east, the Glatzer Neisse, and they have been given the prefixes to differentiate them. Which is an important footnote to history, as much of the discussion at the Potsdam conference centred on whether the German-Polish border should be on the western (Lusatian) or eastern (Glatzer) Neisse rivers.

 * I just looked that second Neisse up, and I discovered there's a third, also in Poland. That's Nysa Szalona (German: Wütende Neiße or Jauersche Neiße).  BTW, I created a link for the Glatzer Neisse in the comment above; the article has the Polish name, Nysa Kłodzka.  140.147.160.78 17:51, 28 June 2007 (UTC)Stephen Kosciesza

By the way, could somebody explain why the Polish, Czech, Sorbian and German names of the river are included in the first para of the article? It makes the whole thing very unreadable, and is probably only of interest to comparative linguistics professors...--Stonemad GB 01:27, 29 July 2006 (UTC)

 * When I look at a map which is not in my language of choice I'd still like to know what I see there. Since that are the languages of that area, it just follows common standards - you wouldn't delete the information on the local name from Munich, would you? --32X 22:42, 10 February 2007 (UTC)

Lusatian Neisse or Nysa Łużycka?
Google Books search:
 * "Lusatian Neisse" + river: 266
 * "Lusatian Neisse" + Poland: 1,140
 * "Lusatian Neisse" + Germany: 1,140
 * Total: 2,5k

 * "Nysa Łużycka" + river: 489
 * "Nysa Łużycka" + Poland: 2,520
 * "Nysa Łużycka" + Germany: 622
 * Total: 3,5k

As such, the "Nysa Łużycka" name seems more popular. --Piotr Konieczny aka Prokonsul Piotrus 01:14, 10 February 2011 (UTC)
 * Looks like you didn't restrict your search to English. Otherwise non-English sources are included. Books in English only:
 * "Lusatian Neisse" + river: 255
 * "Lusatian Neisse" + Poland: 1,020
 * "Lusatian Neisse" + Germany: 1,030
 * Total: 2305
 * "Nysa Łużycka" + river: 414
 * "Nysa Łużycka" + Poland: 823
 * "Nysa Łużycka" + Germany: 461
 * Total: 1698

Karasek (talk) 15:02, 12 March 2011 (UTC)

title: Talk:Lusatian Neisse


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Brian Josephson

Brian David Josephson (born 4 January 1940) is a British theoretical physicist and professor emeritus of physics at the University of Cambridge. Best known for his pioneering work on superconductivity and quantum tunnelling, he was awarded the Nobel Prize in Physics in 1973 for his prediction of the Josephson effect, made in 1962 when he was a 22-year-old PhD student at Cambridge University. Josephson is the first Welshman to have won a Nobel Prize in Physics. He shared the prize with physicists Leo Esaki and Ivar Giaever, who jointly received half the award for their own work on quantum tunnelling.

Josephson has spent his academic career as a member of the Theory of Condensed Matter group at Cambridge's Cavendish Laboratory. He has been a fellow of Trinity College, Cambridge since 1962, and served as professor of physics from 1974 until 2007.

In the early 1970s, Josephson took up transcendental meditation and turned his attention to issues outside the boundaries of mainstream science. He set up the Mind–Matter Unification Project at the Cavendish to explore the idea of intelligence in nature, the relationship between quantum mechanics and consciousness, and the synthesis of science and Eastern mysticism, broadly known as quantum mysticism. He has expressed support for topics such as parapsychology, water memory and cold fusion, which has made him a focus of criticism from fellow scientists.

Education
Josephson was born in Cardiff, Wales, to Jewish parents, Mimi (née Weisbard, 1911–1998) and Abraham Josephson. He attended Cardiff High School, where he credits some of the school masters for having helped him, particularly the physics master, Emrys Jones, who introduced him to theoretical physics. In 1957, he went up to Cambridge, where he initially read mathematics at Trinity College, Cambridge. After completing Maths Part II in two years, and finding it somewhat sterile, he decided to switch to physics.

Josephson was known at Cambridge as a brilliant but shy student. Physicist John Waldram recalled overhearing Nicholas Kurti, an examiner from Oxford, discuss Josephson's exam results with David Shoenberg, reader in physics at Cambridge, and asking: "Who is this chap Josephson? He seems to be going through the theory like a knife through butter." While still an undergraduate, he published a paper on the Mössbauer effect, pointing out a crucial issue other researchers had overlooked. According to one eminent physicist speaking to Physics World, Josephson wrote several papers important enough to assure him a place in the history of physics even without his discovery of the Josephson effect.

He graduated in 1960 and became a research student in the university's Mond Laboratory on the old Cavendish site, where he was supervised by Brian Pippard. American physicist Philip Anderson, also a future Nobel Prize laureate, spent a year in Cambridge in 1961–1962, and recalled that having Josephson in a class was "a disconcerting experience for a lecturer, I can assure you, because everything had to be right or he would come up and explain it to me after class." It was during this period, as a PhD student in 1962, that he carried out the research that led to his discovery of the Josephson effect; the Cavendish Laboratory unveiled a plaque on the Mond Building dedicated to the discovery in November 2012. He was elected a fellow of Trinity College in 1962, and obtained his PhD in 1964 for a thesis entitled Non-linear conduction in superconductors.

Discovery of the Josephson effect
Josephson was 22 years old when he did the work on quantum tunnelling that won him the Nobel Prize. He discovered that a supercurrent could tunnel through a thin barrier, predicting, according to physicist Andrew Whitaker, that "at a junction of two superconductors, a current will flow even if there is no drop in voltage; that when there is a voltage drop, the current should oscillate at a frequency related to the drop in voltage; and that there is a dependence on any magnetic field." This became known as the Josephson effect and the junction as a Josephson junction.

His calculations were published in Physics Letters (chosen by Pippard because it was a new journal) in a paper entitled "Possible new effects in superconductive tunnelling," received on 8 June 1962 and published on 1 July. They were confirmed experimentally by Philip Anderson and John Rowell of Bell Labs in Princeton; this appeared in their paper, "Probable Observation of the Josephson Superconducting Tunneling Effect," submitted to Physical Review Letters in January 1963.

Before Anderson and Rowell confirmed the calculations, the American physicist John Bardeen, who had shared the 1956 Nobel Prize in Physics (and who shared it again in 1972), objected to Josephson's work. He submitted an article to Physical Review Letters on 25 July 1962, arguing that "there can be no such superfluid flow." The disagreement led to a confrontation in September that year at Queen Mary College, London, at the Eighth International Conference on Low Temperature Physics. When Bardeen (then one of the most eminent physicists in the world) began speaking, Josephson (still a student) stood up and interrupted him. The men exchanged views, reportedly in a civil and soft-spoken manner. See also:.

Whitaker writes that the discovery of the Josephson effect led to "much important physics," including the invention of SQUIDs (superconducting quantum interference devices), which are used in geology to make highly sensitive measurements, as well as in medicine and computing. IBM used Josephson's work in 1980 to build a prototype of a computer that would be up to 100 times faster than the IBM 3033 mainframe.

Nobel Prize

Josephson was awarded several important prizes for his discovery, including the 1969 Research Corporation Award for outstanding contributions to science, and the Hughes Medal and Holweck Prize in 1972. In 1973 he won the Nobel Prize in Physics, sharing the $122,000 award with two other scientists who had also worked on quantum tunnelling. Josephson was awarded half the prize "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects". The other half of the award was shared equally by Japanese physicist Leo Esaki of the Thomas Watson Research Center in Yorktown, New York, and Norwegian-American physicist Ivar Giaever of General Electric in Schenectady, New York.

Positions held
Josephson spent a postdoctoral year in the United States (1965–1966) as research assistant professor at the University of Illinois at Urbana–Champaign. After returning to Cambridge, he was made assistant director of research at the Cavendish Laboratory in 1967, where he remained a member of the Theory of Condensed Matter group, a theoretical physics group, for the rest of his career. He was elected a Fellow of the Royal Society (FRS) in 1970, and the same year was awarded a National Science Foundation fellowship by Cornell University, where he spent one year. In 1972 he became a reader in physics at Cambridge and in 1974 a full professor, a position he held until he retired in 2007.

A practitioner of Transcendental Meditation (TM) since the early seventies, Josephson became a visiting faculty member in 1975 of the Maharishi European Research University in the Netherlands, part of the TM movement. He also held visiting professorships at Wayne State University in 1983, the Indian Institute of Science, Bangalore in 1984, and the University of Missouri-Rolla in 1987.

Early interest and Transcendental Meditation

Josephson became interested in philosophy of mind in the late sixties and, in particular, in the mind–body problem, and is one of the few scientists to argue that parapsychological phenomena (telepathy, psychokinesis and other paranormal themes) may be real. In 1971, he began practising Transcendental Meditation (TM), which had been taken up by several celebrities, including the Beatles.

Winning the Nobel Prize in 1973 gave him the freedom to work in less orthodox areas, and he became increasingly involved – including during science conferences, to the irritation of fellow scientists – in talking about meditation, telepathy and higher states of consciousness. In 1974, he angered scientists during a colloquium of molecular and cellular biologists in Versailles by inviting them to read the Bhagavad Gita (5th – 2nd century BCE) and the work of Maharishi Mahesh Yogi, the founder of the TM movement, and by arguing about special states of consciousness achieved through meditation. "Nothing forces us," one scientist shouted at him, "to listen to your wild speculations." Biophysicist Henri Atlan wrote that the session ended in uproar.

In May that year, Josephson addressed a symposium held to welcome the Maharishi to Cambridge. The following month, at the first Canadian conference on psychokinesis, he was one of 21 scientists who tested claims by Matthew Manning, a Cambridgeshire teenager who said he had psychokinetic abilities; Josephson apparently told a reporter that he believed Manning's powers were a new kind of energy. He later withdrew or corrected the statement.

Josephson said that Trinity College's tradition of interest in the paranormal meant that he did not dismiss these ideas out of hand. Several presidents of the Society for Psychical Research had been fellows of Trinity, and the Perrott-Warrick Fund, set up in Trinity in 1937 to fund parapsychology research, is still administered by the college. He continued to explore the idea that there is intelligence in nature, particularly after reading Fritjof Capra's The Tao of Physics (1975), and in 1979 took up a more advanced form of TM, known as the TM-Sidhi program. According to Anderson, the TM movement produced a poster showing Josephson levitating several inches above the floor. Josephson argued that meditation could lead to mystical and scientific insights, and that, as a result of it, he had come to believe in a creator.

Fundamental Fysiks Group

Josephson became involved in the mid-1970s with a group of physicists associated with the Lawrence Berkeley Laboratory at the University of California, Berkeley, who were investigating paranormal claims. They had organized themselves loosely into the Fundamental Fysiks Group, and had effectively become the Stanford Research Institute's (SRI) "house theorists," according to historian of science David Kaiser. Core members in the group were Elizabeth Rauscher, George Weissmann, John Clauser, Jack Sarfatti, Saul-Paul Sirag, Nick Herbert, Fred Alan Wolf, Fritjof Capra, Henry Stapp, Philippe Eberhard and Gary Zukav.

There was significant government interest at the time in quantum mechanics – the American government was financing research at SRI into telepathy – and physicists able to understand it found themselves in demand. The Fundamental Fysiks Group used ideas from quantum physics, particularly Bell's theorem and quantum entanglement, to explore issues such as action at a distance, clairvoyance, precognition, remote viewing and psychokinesis.

In 1976, Josephson travelled to California at the invitation of one of the Fundamental Fysiks Group members, Jack Sarfatti, who introduced him to others including laser physicists Russell Targ and Harold Puthoff, and quantum physicist Henry Stapp. The San Francisco Chronicle covered Josephson's visit.

Josephson co-organized a symposium on consciousness at Cambridge in 1978, publishing the proceedings as Consciousness and the Physical World (1980), with neuroscientist V. S. Ramachandran. A conference on "Science and Consciousness" followed a year later in Cordoba, Spain, attended by physicists and Jungian psychoanalysts, and addressed by Josephson, Fritjof Capra and David Bohm (1917–1992).

By 1996, he had set up the Mind–Matter Unification Project at the Cavendish Laboratory to explore intelligent processes in nature. In 2002, he told Physics World: "Future science will consider quantum mechanics as the phenomenology of particular kinds of organised complex system. Quantum entanglement would be one manifestation of such organisation, paranormal phenomena another."

Reception and views on the scientific community
Josephson delivered the Pollock Memorial Lecture in 2006, the Hermann Staudinger Lecture in 2009 and the Sir Nevill Mott Lecture in 2010.

Matthew Reisz wrote in Times Higher Education in 2010 that Josephson has long been one of physics' "more colourful figures." His support for unorthodox causes has attracted criticism from fellow scientists since the 1970s, including from Philip Anderson. Josephson regards the criticism as prejudice, and believes that it has served to deprive him of an academic support network.

He has repeatedly criticized "science by consensus," arguing that the scientific community is too quick to reject certain kinds of ideas. "Anything goes among the physics community – cosmic wormholes, time travel," he argues, "just so long as it keeps its distance from anything mystical or New Age-ish." Referring to this position as "pathological disbelief," he holds it responsible for the rejection by academic journals of papers on the paranormal. He has compared parapsychology to the theory of continental drift, proposed in 1912 by Alfred Wegener (1880–1930) to explain observations that were otherwise inexplicable, which was resisted and ridiculed until evidence led to its acceptance after Wegener's death.

Science writer Martin Gardner criticized Josephson in 1980 for complaining to The New York Review of Books, along with three other physicists, about an article by J. A. Wheeler that ridiculed parapsychology. Several physicists complained in 2001 when, in a Royal Mail booklet celebrating the Nobel Prize's centenary, Josephson wrote that Britain was at the forefront of research into telepathy. Physicist David Deutsch said the Royal Mail had "let itself be hoodwinked" into supporting nonsense, although another physicist, Robert Matthews, suggested that Deutsch was skating on thin ice given the latter's own work on parallel universes and time travel.

In 2004, Josephson criticized an experiment by the Committee for Skeptical Inquiry to test claims by Russian schoolgirl Natasha Demkina that she could see inside people's bodies using a special kind of vision. The experiment involved her being asked to match six people to their confirmed medical conditions (plus one with none); to pass the test she had to make five correct matches, but made only four. Josephson argued that this was statistically significant, and that the experiment had set her up to fail. One of the researchers, Richard Wiseman, professor of psychology at the University of Hertfordshire, responded by highlighting that the conditions of the experiment had been agreed to before it started, and the potential significance of her claims warranted a higher than normal bar. Keith Rennolis, professor of applied statistics at the University of Greenwich, supported Josephson's position, asserting that the experiment was "woefully inadequate" to determine any effect.

Josephson's reputation for promoting unorthodox causes was cemented by his support for the ideas of water memory and cold fusion, both of which are rejected by mainstream scientists. Water memory is purported to provide a possible explanation for homeopathy; it is dismissed by scientists as pseudoscience, although Josephson has expressed support for it since attending a conference at which French immunologist Jacques Benveniste first proposed it. Cold fusion is the hypothesis that nuclear reactions can occur at room temperature. When Martin Fleischmann, the British chemist who pioneered research into it, died in 2012, Josephson wrote a supportive obituary in the Guardian, and had published in Nature a letter complaining that its obituary had failed to give Fleischmann due credit. Antony Valentini of Imperial College London withdrew Josephson's invitation to a 2010 conference on the de Broglie-Bohm theory because of his work on the paranormal, although it was reinstated after complaints.

Josephson's defense of paranormal claims and of cold fusion have led him to being described as an exemplar of a sufferer of the hypothetical Nobel disease.

Awards

 * £1,000 New Scientist prize, 1969
 * Research Corporation Award for outstanding contributions to science, 1969
 * Elected a Fellow of the Royal Society (FRS) in 1970
 * Fritz London Memorial Prize, 1970
 * Guthrie Medal (Institute of Physics), 1972
 * Van der Pol medal, International Union of Radio Science, 1972
 * Elliott Cresson Medal (Franklin Institute), 1972
 * Hughes Medal, 1972
 * Holweck Prize (Institute of Physics and French Institute of Physics), 1972
 * Nobel Prize in Physics, 1973
 * Honorary doctorate, University of Wales, 1974
 * Faraday Medal (Institution of Electrical Engineers), 1982
 * Honorary doctorate, University of Exeter, 1983
 * Sir George Thomson (Institute of Measurement and Control), 1984

Selected works

 * (2012). "Biological Observer-Participation and Wheeler's 'Law without Law'," in Plamen L. Simeonov, Leslie S. Smith and Andrée C. Ehresmann (eds.), Integral Biomathics, Springer, pp. 244–252.
 * (2005). "Foreword," in Michael A. Thalbourne and Lance Storm (eds.), Parapsychology in the Twenty-First Century, McFarland, pp. 1–2.
 * (2003). "We Think That We Think Clearly, But That's Only Because We Don't Think Clearly," in Patrick Colm Hogan and Lalita Pandit (eds.), Rabindranath Tagore: Universality and Tradition, Fairleigh Dickinson University Press, pp. 107–115.
 * (2003). "String Theory, Universal Mind, and the Paranormal", arXiv, physics.gen-ph, 2 December 2003.
 * (2002). "Beyond quantum theory: A realist psycho-biological interpretation of reality’ revisited", Biosystems, 64(1–3), January, pp. 43–45.
 * (2000). "Positive bias to paranormal claims", Physics World, October.
 * (1999). "What is truth?, Physics World, February.
 * (1997). "Skeptics cornered", Physics World, September.
 * (1997). "What is Music a Language For?" in Paavo Pylkkänen, Pauli Pylkkö, and Antti Hautamäki (eds.), Brain, Mind and Physics, IOS Press, pp. 262–265.
 * (1996). "Consciously avoiding the X-factor", Physics World, December.
 * with Jessica Utts (1996). "Do you believe in psychic phenomena? Are they likely to be able to explain consciousness?", Times Higher Education, 8 April.
 * with Tethys Carpenter (1996). "What can Music tell us about the Nature of the Mind? A Platonic Model," in Stuart R. Hameroff, Alfred W. Kaszniak and Alwyn Scott (eds.), Toward a Science of Consciousness, MIT Press, pp. 691–694.
 * with Colm Wall and Anthony Clark (1995). "Light Barrier", New Scientist, 29 April.
 * (1994). "Awkward Eclipse", New Scientist, 17 December.
 * (1994). BBC 'Heretic' series", Times Higher Education Supplement, 12 August.
 * with Beverly A. Rubik (1992). "The challenge of consciousness research", Frontier Perspectives, 3(1), pp. 15–19.
 * with Fotini Pallikari-Viras (1991). "Biological Utilization of Quantum Nonlocality", Foundations of Physics, 21(2), pp. 197–207 (also available here).
 * (1990). "The History of the Discovery of Weakly Coupled Superconductors," in John Roche (ed.), Physicists Look Back: Studies in the History of Physics, CRC Press, p. 375.
 * (1988). "Limits to the universality of quantum mechanics", Foundations of Physics, 18(12), December, pp. 1195–1204.
 * with M. Conrad and D. Home (1987). "Beyond Quantum Theory: A Realist Psycho-Biological Interpretation of Physical Reality," in Alwyn van der Merwe, Franco Selleri and Gino Tarozzi (eds.), Microphysical Reality and Quantum Formalism, Springer, 1987, p. 285ff.
 * with D.E. Broadbent (1981). "Perceptual Experiments and Language Theories", Philosophical Transactions of the Royal Society, 295(10772), October, pp. 375–385.
 * with H. M. Hauser (1981). "Multistage Acquisition of Intelligent Behaviour", Kybernetes, 10(1).
 * with V. S. Ramachandran (eds.) (1980). Consciousness and the Physical World, Pergamon Press.
 * with Richard D. Mattuck, Evan Harris Walker and Olivier Costa de Beauregard (1980). "Parapsychology: An Exchange", New York Review of Books, 27, 26 June, pp. 48–51.
 * (1979). "Foreword," in Andrija Puharich (ed.), The Iceland Papers: Select Papers on Experimental and Theoretical Research on the Physics of Consciousness, Essentia Research Associates.
 * (1978). "A Theoretical Analysis of Higher States of Consciousness and Meditation", Current Topics in Cybernetics and Systems, pp. 3–4.
 * (1974). "The Artificial Intelligence/Psychology Approach to the Study of the Brain and Nervous System", Lecture Notes in Biomathematics, 4, pp. 370–375.
 * (1974). "Magnetic field dependence of the surface reactance of superconducting tin at 174 MHz", Journal of Physics F: Metal Physics, 4(5), May, p. 751.
 * (1973). "The Discovery of Tunnelling Supercurrents", Science, Nobel lecture, 12 December, pp. 157–164.
 * (1969). "Equation of state near the critical point", Journal of Physics C: Solid State Physics, 2(7), July.
 * with J. Lekner (1969). "Mobility of an Impurity in a Fermi Liquid", Physical Review Letters. 23(3), pp. 111–113.
 * (1967). "Inequality for the specific heat: II. Application to critical phenomena", Proceedings of the Physical Society, 92(2), October.
 * (1967). "Inequality for the specific heat: I. Derivation", Proceedings of the Physical Society, 92(2), October.
 * (1966). "Macroscopic Field Equations for Metals in Equilibrium", Physical Review, 152, December, pp. 211–217.
 * (1966). "Relation between the superfluid density and order parameter for superfluid He near Tc", Physics Letters, 21(6), 1 July, pp. 608–609.
 * (1965). "Supercurrents through Barriers", Advances in Physics, 14(56), pp. 419–451.
 * (1964). Non-linear conduction in superconductors, (PhD thesis), University of Cambridge, December.
 * (1964). "Coupled Superconductors", Review of Modern Physics, 36(1), pp. 216–220.
 * (1962). "The Relativistic Shift in the Mössbauer Effect and Coupled Superconductors", submitted for Trinity College fellowship.
 * (1962). "Possible new effects in superconductive tunnelling", Physics Letters, 1(7), 1 July, pp. 251–253.
 * (1960). "Temperature-dependent shift of gamma rays emitted by a solid", Physical Review Letters, 4, 1 April.

title: Brian Josephson


text:
Letters to the inhabitants of Canada

The Letters to the inhabitants of Canada were three letters written by the First and Second Continental Congresses in 1774, 1775, and 1776 to communicate directly with the population of the Province of Quebec, formerly the French province of Canada, which had no representative system at the time. Their purpose was to draw the large French-speaking population to the American revolutionary cause. This goal ultimately failed, and Quebec, along with the other northern provinces of British America, remained loyal to Britain. The only significant assistance that was gained was the recruitment of two regiments totalling not more than 1,000 men.

Background
The acquisition of the Province of Quebec as a result of the French and Indian War (1754–1763) gave Great Britain control over nearly the entire eastern seaboard of North America, and brought the former French colony of Canada into a closer relationship with the American colonies. The new province was significantly different from the other provinces of British America, as the vast majority of people in Quebec spoke only French and were Roman Catholic. There were also differences in civic and legal affairs, as the law had, prior to the British conquest, been based on French law.

In 1774, the British Parliament enacted the Quebec Act, along with other legislation that was labeled by American colonists as the Intolerable Acts. This measure, which replaced the Royal Proclamation of 1763 as the governing document of Quebec, was used to fortify the position of the British in Quebec by guaranteeing (among other things) the rights of French Canadians to practice Roman Catholicism. It is largely perceived by historians to be damage control in the province of Quebec, in order to prevent the French Canadians from joining the independence movement in the American colonies. The American colonists interpreted the religious provisions concerning Catholicism as a wedge by which Catholicism might be introduced into all of the colonies, and other provisions concerning the structure of the Quebec government to be an attempt by the British Parliament to assert more control over the province, and deny its people what many considered to be basic rights.

Congress drafts the letter
On October 21, 1774, the First Continental Congress, meeting to craft a united response to the Intolerable Acts, resolved to address letters to the populations of Quebec, St. John's Island, Nova Scotia, Georgia, East Florida and West Florida, all being colonies that were not represented by delegates in the Congress. A committee composed of Thomas Cushing, Richard Henry Lee and John Dickinson was set up to draft those letters. A first draft was presented on October 24, debated and returned to the committee. On October 26, a new draft was presented, debated, amended and adopted. A resolution was passed for the president to sign the letter and ordering the translation and printing of a Letter to the Inhabitants of the Province of Quebec to be done under the supervision of the delegates of Pennsylvania. The letter was translated to French and printed as an 18-page brochure entitled Lettre adressée aux habitans de la Province de Québec, ci-devant le Canada, de la part du Congrès général de l'Amérique Septentrionale, tenu à Philadelphie. The translation is attributed to Pierre Eugene du Simitiere. The final content of the letter is attributed to John Dickinson, as a draft in his own hand very closely resembles the final letter.

Contents of the first letter
The letter informed the people of Quebec of five important rights of British constitutional law which were not in force in their colony over a decade after the peace treaty of 1763, which ended the French and Indian War, and resulted in every French subject in Canada becoming a new British subject, theoretically equal in rights to all other British subjects. These five rights were representative government, trial by jury, Habeas Corpus, land ownership, and freedom of the press. The text quotes a passage of Beccaria's On Crimes and Punishment and multiple excerpts of Montesquieu's The Spirit of Laws. Quebec historian Marcel Trudel believes this first letter to have been "a crash course on democratic government", while Gustave Lanctôt claims that the Congress' letter "introduced [among the inhabitants] the notion of personal liberty and political equality.", calling it their first "political alphabet" and "first lesson in constitutional law".

The people of Quebec were invited to give themselves the provincial representation the Quebec Act did not provide for, and have this representative body send delegates to the upcoming continental Congress, to be held in Philadelphia on May 10, 1775.

Distribution and reaction to the first letter
The French-born Philadelphia printer Fleury Mesplet printed 2,000 copies of the French translation. Other manuscript French translations of the original English letter (first published in Dunlap's Pennsylvania Packet) were in circulation as well, possibly even arriving in Canada before the "official" translation paid by the Congress. Wide circulation of the letter was prevented by General Guy Carleton, then Governor of the province. However, he reported to his superiors in England that, "a report was spread that at Montreal that letters of importance had been received from the General Congress," and that town meetings were being held, "breathing that same spirit, so plentifully gone forth through the neighbouring Provinces." These town meetings, seemingly dominated by English-speakers, ended without the election of delegates to the Continental Congress.

In early 1775, Boston's Committee of Correspondence sent John Brown into Quebec to gather intelligence, gauge sentiment, and agitate for rebellion in that province. He found mixed sentiment among English-speaking inhabitants, some of whom were concerned that the Congress' adoption of an export boycott would essentially give the lucrative fur trade to French-speakers. The bulk of the French-speaking population was at best neutral with respect to British rule; some were happy with it, but more might be convinced to assist the Americans in their aims. Brown also noted the relatively weak military presence in the province. General Carleton, while aware of Brown's activities, did nothing to interfere, beyond preventing publication of the letter in the local newspaper.

Drafting the second letter
The Second Continental Congress met on May 10, 1775, following the Battles of Lexington and Concord in which colonial forces resisted a large British force on April 19 and drove it back to Boston. This victory resulted in Congress opening the session with great excitement and hope.

John Brown arrived in Philadelphia on May 17 to report the capture of Fort Ticonderoga and the raid on Fort Saint-Jean, an event that stimulated much discussion in the Congress. On May 26, the Congress resolved to draft a second letter to the inhabitants of Canada. The committee that drafted the letter was composed of John Jay, Silas Deane and Samuel Adams, the last having previously written a letter to the people of Canada on behalf of the Boston Committee of Correspondence. On May 29, after having heard additional testimony on the situation in Montreal from James Price, a Montreal merchant, the Second Continental Congress approved the letter.

The letter, entitled Letter to the oppressed inhabitants of Canada, was translated as Lettre adressée aux habitants opprimés de la province de Québec, de la part du Congrès général de l’Amérique septentrionale, tenu à Philadelphie. The letter was signed by president John Hancock, and again translated by Pierre Eugène du Simitière; 1,000 copies of it were printed by Fleury Mesplet. The content of the letter has been attributed to John Jay.

Contents of the second letter
In the letter, the Congress again deplored the form of the civil government introduced by the Quebec Act, which it likened to "tyranny". It further asserted that under this form of government "you and your wives and your children are made slaves." As for the enjoyment of their religion, the Congress believed it uncertain for it depended on "a legislature in which you have no share, and over which you have no controul [sic]". The Congress was clearly hoping to draw French-speaking habitants to their cause, as well as English-speaking residents that had migrated to Quebec from the other colonies.

At the time of the letter's writing, the Congress was already aware that Governor Carleton had called the people to arm themselves to defend their new King from the invasion. The letter warned the population of the danger of being sent to fight against France were it to join the war on the side of the Americans (which it eventually did in 1778). If the Congress insisted again on treating the Canadians as friends sharing common interests with the other colonists, it however warned the people not to "reduce us the disagreeable necessity of treating you as enemies."

Distribution and reaction to the second letter
Price took the letter to Montreal, along with a similar letter from the New York Provincial Congress, and circulated them in the province. Much of the English-speaking merchant class, which was dependent on the fur trade and the market for it in Europe, was wary of the situation. The French habitants were generally unswayed by appeals to English liberties, with which they had relatively little familiarity. However, they were also not overly supportive of the existing military government, as calls to arms were met with limited success. The habitants much more opportunistically were happy to follow whichever force was winning at the time, as long as they paid for their supplies.

In the end, the Americans gained limited support in Quebec, ultimately raising two regiments that participated in the Continental Army. The 1st Canadian Regiment was raised in November 1775 during the early days of the invasion of Canada, and the 2nd Canadian Regiment was raised in January 1776.

Third letter
In September 1775, after the failure of the second letter to sway public opinion, the American Colonists launched an invasion of Quebec from Fort Ticonderoga and Cambridge, Massachusetts. This invasion culminated in the Battle of Quebec at the end of December 1775, in which the city was successfully defended, and the invaders dug in for the winter. Following the battle, Moses Hazen and Edward Antill traveled from Quebec to Philadelphia to bring the news of the American defeat.

Drafting the third letter
After hearing of the defeat, the Congress, on January 23, 1776, set up a committee to which was entrusted the drafting of another letter to the Canadian population. The members of the committee this time were William Livingston, Thomas Lynch Jr, and James Wilson. The letter was approved the day after, and signed by John Hancock.

Contents
The Congress thanked the population for the services it rendered to its cause and ensured them that troops to protect them were on the way, and would arrive before British reinforcements. It also informed them that the Congress had authorized the raising of two battalions in Canada to assist in the cause. The people were once again invited to organize local and provincial assemblies, which could choose delegates to represent the province in the Continental Congress.

Distribution and reaction to the third letter
The French translation was again printed by Fleury Mesplet; however, it is not certain who in the committee is the author and also if du Simitière was the translator. Hazen and Antill delivered copies of the letter to David Wooster, commanding the colonial forces occupying Montreal. He oversaw distribution of the letter at the end of February.

The letter met with no significant response, as the populace was unhappy about being paid for supplies in paper currency, and was otherwise not enamoured of the occupation by the colonial forces.

Conclusion
The 1775 American invasion was a disastrous failure, with the Americans forced to retreat back to Fort Ticonderoga. The province remained in British hands, and its population centers were never threatened again in the war. The goal of these letters, and a variety of other addresses to the Canadian people, to gain political and military support for the revolution were generally not realized. While the Congress succeeded in raising two regiments of Canadians (James Livingston's 1st Canadian Regiment and Hazen's 2nd Canadian Regiment), their numbers were not as large as desired, and the seigneurs and the Catholic clergy ultimately rallied around the British governor. Quebec would remain a relatively strong colony for Britain due in large part to the strict leadership of Guy Carleton, and despite attempts to bring the revolutionary spirit of the American colonies into Quebec.

Contents of the letters
English and French Wikisource have the contents of the letters:
 * Letter to the Inhabitants of the Province of Quebec, October 26, 1774 (en, fr)
 * Letter to the oppressed inhabitants of Canada, May 29, 1775 (en, fr)
 * Letter to the Inhabitants of the Province of Canada, January 24, 1776 (en, fr)

title: Letters to the inhabitants of Canada


text:
Mr. Hooper

Mr. Harold Hooper (played by Will Lee) was one of the first four human characters to appear on the television series Sesame Street. Created by producer and writer Jon Stone, Mr. Hooper is the original proprietor of Hooper's Store, the neighborhood variety store and combination diner/corner store that serves as a place for Muppets and humans to meet and interact. Lee, a character actor and instructor was "perfectly cast" as Mr. Hooper. Mr. Hooper ranked first of all human characters of the show in recognition by young viewers. Mr. Hooper, who has been described as "slightly cranky but good-hearted" and "curmudgeonly", bridges the gap between the older generation and its young audience. Hooper's Store, "an idealized social institution", is an extension of his personality. He had a close relationship with the Muppet Big Bird.

After Lee's death on December 7, 1982, instead of recasting the role, or explaining his departure by saying he had moved, quit or retired, the writers and producers of Sesame Street decided to have the character of Mr. Hooper die. Then, they created a TV episode to teach their young audience about the difficult topic of death. Research was conducted to ascertain the messages they wanted to convey about the topic, as well as the effect the episode would have on the young children who watched it. They were advised by experts in the fields of child psychology, child development, and religion. Studies conducted after the episode was produced showed that most children understood its messages about death, and that they experienced no long-term ill effects.

The episode, written by head writer Norman Stiles, aired on Thanksgiving Day 1983. The cast and crew reported that filming it was an emotional and touching experience, with Bob McGrath listing it as one of his two favorites. Setting the standard for dealing with difficult topics on children's television, the show was called heartbreaking yet affirming, and remains one of the proudest moments in the show's history.

Development and description
Mr. Hooper, played by Will Lee from the premiere of Sesame Street in 1969 until his death in 1982, was one of the first four human characters that appeared on the show. Created by producer and writer Jon Stone, the role of Mr. Hooper was the first to be cast. Lee came to Stone's attention through writers Bruce Hart and Carole Hart. Mr. Hooper was inspired by the Bob Keeshan character Captain Kangaroo; Stone previously worked on the Captain Kangaroo program, which greatly influenced him as he developed Sesame Street. Mr. Hooper is the original proprietor of Hooper's Store, the neighborhood variety store and combination diner/corner store that serves as a place for Muppets and humans to meet and interact. Stone's original conception of Mr. Hooper was that he would be, like most owners of such establishments at the time, older, male, and Jewish.

Lee was a character actor and acting instructor with a range of roles in the theater. Lee had been blacklisted from many mainstream acting roles for about five years during the McCarthy era, for refusing to cooperate with the House Un-American Activities Committee's investigation of Communist influence in show business. According to writer Michael Davis, Lee played Mr. Hooper, known for his bowtie and horn-rimmed glasses, "with such certainty and naturalness he made adults suspend their sense of disbelief". Writer Louise A. Gikow stated that Lee was "perfectly cast" as Mr. Hooper. According to fellow cast member Bob McGrath, who also appeared in Sesame Street 's first episode with Lee, "Will had a broader dimension to his character than perhaps the rest of us did ... He convinced me that no matter how simple the scene was with a child, you had to bring a tremendous integrity and an honesty and credibility to it". Joan Ganz Cooney, Sesame Street co-creator and president of the Children's Television Workshop (CTW), said, "He gave millions of children the message that the old and the young have a lot to say to each other". The New York Times reported that Mr. Hooper ranked first of all human characters of the show in recognition by young viewers.

Davis described Mr. Hooper as "slightly cranky but good-hearted". Gikow called Mr. Hooper "curmudgeonly". Davis stated that since Mr. Hooper's appearance in the first episode of Sesame Street, he had become many things to many young children, "... the guy in the apron at the far side of the generation gap, his half-lens glasses slipping down his nose". Davis also stated that Hooper's Store, which he called "an idealized social institution", is an extension of Mr. Hooper's personality. Mr. Hooper has a special relationship with the Muppet character Big Bird, who would often come into Hooper's Store for a birdseed milkshake and a chat. A running gag in the show was that Big Bird would often mispronounce Mr. Hooper's name, although most attempts ended in "ooper", such as "Looper" or "Cooper". Mr. Hooper's first name, Harold, was not revealed until the character earned a GED during night school.

Mr. Hooper's last appearances on Sesame Street aired in 1983, but Lee's last segments for the show were taped in November 1982. Lee participated in the Macy's Thanksgiving Day Parade with other Sesame Street characters a few days before he died of a heart attack on December 7, 1982.

Death of Mr. Hooper
When Will Lee died on December 7, 1982, instead of recasting the role for the character (replacing Will Lee with a new actor so Mr. Hooper could still be in the show), explaining Mr. Hooper's departure (by saying that he had retired and/or moved away), or simply dropping him from the show without explanation, the producers of Sesame Street decided to have the character pass away as well. Then they used the episode to teach their young audience about the difficult topic of death. According to CTW researcher Rosemarie Truglio and her colleagues, the episode was one of the many social issues relevant to preschoolers the show has dealt with throughout its history. Executive producer Dulcy Singer reported that they followed their instincts to be "honest and straightforward" and to "deal with it head-on".

Synopsis
The Sesame Street episode (#1839) in which the death of Mr. Hooper was discussed, was structured as all episodes were structured at the time, with individual segments that took place on the main brownstone set interrupted by inserts, or puppet skits, short films, and animations. The episode begins with a scene between Gordon (Roscoe Orman) and the Muppet Forgetful Jones (Richard Hunt). Gordon helps Forgetful remember something that had made him happy; as Davis states, "Later, Big Bird forgets something that makes him sad". After several inserts, Big Bird walks backward with his head between his legs; when Gordon asks him why, he answers, "Just because". Later, Big Bird listens to the adults talking about a new baby who is due to visit Sesame Street with his mother.

Two segments later, Big Bird interrupts the adults—Maria (Sonia Manzano), David (Northern Calloway), Bob (Bob McGrath), Susan (Loretta Long), Gordon, Luis (Emilio Delgado), and Olivia (Alaina Reed Hall)—discussing politics by giving them pictures he had drawn of each of them. He gets to Mr. Hooper's picture, saying that he will give it to him when he returns. The human characters explain the irreversibility of death to Big Bird, who reacts by getting upset, expressing his confusion and sadness. The adults reassure him that they love him and will take care of him. David reveals that he will take over the store, Mr. Hooper having left it to him in his will, and that he is going to serve milkshakes to Big Bird, like Mr. Hooper used to do. Big Bird asks, "Why does it have to be this way? Give me one good reason!" and after a long silence Gordon answers, "Big Bird, it has to be this way... because." Looking at Mr. Hooper's picture, Big Bird says, mispronouncing his name as he had done many times in the past, "I'm going to miss you, Mr. Looper." Maria tearfully corrects Big Bird and everyone gathers around him, hugging him in support.

The episode ends with Big Bird hanging Mr. Hooper's picture near his nest. Luis knocks on his door to introduce the new baby, followed by the entire grown-up cast. Big Bird says, "You know what the nice thing is about new babies? One day they're not here, and the next day, here they are!" The cast collectively show affection to the baby as the show closes.

Research
Similar to what they had done with other social issues and in developing their curriculum, the CTW researched the topic of death and how preschoolers understand it. The first step in their research process was to assemble a team of experts, led by CTW research director Lewis Bernstein, in the fields of child psychology, child development, and religion. The team advised the show's writers and producers how to handle the topic, in what they called "a curriculum bath"; Bernstein described it in this way: "We bring in the experts to allow the writer to soak in expertise. We in Research bring in people to provide the information, and then the artistry of the writer takes over, as they integrate what they've heard". The experts advised the producers to provide their viewers with a sense of closure about Mr. Hooper's death. They decided not to focus on how Mr. Hooper died, since explaining that he was old and ill might increase children's fears about death. They chose to deal with his death in a single episode, and convey simple messages like: "Mr. Hooper is dead; Mr. Hooper will not be coming back; and Mr. Hooper will be missed by all". Gikow stated that the episode they created was an example of the writers and producers' skills as educators as well as entertainers.

Before the episode aired, the CTW conducted a series of studies to guide the writers and producers in creating the episode. Their goal was to answer four key questions: (1) Will children understand the messages they wanted to convey about death? (2) How attentive will they be to the storyline? (3) How will parents respond to the treatment of such a sensitive topic? and (4) Will children be disturbed by the messages, and if so, for how long? The researchers broke up children into three groups: children who only watched the scenes in which the storyline was played out and who were interviewed afterwards; children who watched the entire episode and whose attention was recorded while they viewed it; and children who watched the episode without the inserts, with their parents, who were interviewed 9 or 10 days later.

The researchers found that 73% of 4- and 5-year-olds in their study understood that Mr. Hooper was dead and that 88% of this group understood that he was not coming back, although only about one-fourth of the 3-year-old viewers responded correctly. Most of the 4- and 5-year-olds understood that Big Bird and the adults were sad. Most children (80%) were attentive during the episode. The parents interviewed had "overwhelmingly positive" reactions to the show, and that half reported that they had discussed death with their children after viewing it. None of the parents reported negative reactions from their children, either immediately after watching the episode or at a later time.

Development and legacy
Sesame Street head writer Norman Stiles was chosen to write the segments about Mr. Hooper's death. The episode focused on the life cycle of birth and death by also mentioning the birth of a baby, and by remembering Mr. Hooper. Stiles said, "We decided to say that while Mr. Hooper was not here anymore, we will always have that part of him that lives within the heart, that we have our love and that it will always stay". Stiles wanted to convey that expressing grief for someone who had died was difficult for both adults and children. Instead of providing an explanation, the adults of Sesame Street tell Big Bird, when he asked why Mr. Hooper had died, that there was no real reason, that it happened, as Gordon tells Big Bird, "Just because". The show's outside experts advised Stiles and the producers to remove the line because they were concerned that an open-ended explanation would not be enough for children, but Stiles kept the line because it was an acknowledgement, as Gikow stated, that there is "never a good explanation" about why people die.

The episode aired on Thanksgiving Day 1983, a year after Lee's final appearance as Mr. Hooper at the Macy's Thanksgiving Day parade. The producers chose to air it the first week of the new season in order to explain Mr. Hooper's absence as soon as possible, for maximum exposure, and to ensure that parents were at home with their children in order to discuss it. The illustrations used for the episode were drawn by Caroll Spinney, who performed Big Bird. Mr. Hooper's picture remained on the set from then on, as a continuing memorial to Lee and Mr. Hooper. Spinney, speaking of the scene in which the pictures were passed out, reported, "When we finished that scene there wasn't one of us whose face wasn't streaked with tears", even Spinney underneath his costume. Jon Stone, who directed the episode, wanted to do another take, although Spinney later said, "There was nothing wrong with that take. It was perfect." Cameraman Frankie Biondo was touched by the performance.

A book, entitled I'll Miss You, Mr. Hooper and based upon the script for the episode, was published in 1984. The book was also written by Stiles. According to Renée Cherow-O'Leary, Stiles and the editorial staff of the CTW's book division worked with the show's research staff and used the same educational content information and research the show's producers used to create the episode.

title: Mr. Hooper


text:
Hans-Rudolf Merz

Hans-Rudolf Merz (born 10 November 1942) is a Swiss politician who served as a Member of the Swiss Federal Council from 2004 to 2010. A member of the Free Democratic Party (FDP/PRD) until the foundation of FDP.The Liberals in 2009, he headed the Federal Department of Finance during his tenure as a Federal Councillor. Merz served as President of the Swiss Confederation in 2009.

Education
Born in Herisau in the canton of Appenzell Ausserrhoden, he studied at Hochschule St. Gallen and graduated in 1971 with a DEA's degree. Merz was a Scout and visited the National Jamboree of Switzerland in July 2008. He is married and a father of three sons.

Early political career
From 1969 to 1974, he was party secretary of the Free Democratic Party (FDP/PRD) in St. Gallen. From 1974 to 1977 he worked as vice president for UBS's Wolfsberg formation centre in Ermatingen. Since then he has worked as a management consultant. In 1997 he was elected to the Swiss Council of States for the canton of Appenzell Ausserrhoden. He presided over the finance committee and was a member of the foreign policy committee.

Swiss Federal Council
Merz was elected to the Swiss Federal Council on 10 December 2003 and took office on 1 January 2004. At the time he was on the board of directors of the Helvetia-Patria insurance company and Anova Holding. He was also a member of the board of trustees of the Max Schmidheiny Foundation.

On 20 September 2008, whilst in Eastern Switzerland, Merz was rushed to hospital, having suffered from a heart attack. He was soon flown to Bern University Hospital, where he had a multiple bypass operation. He was also placed into an artificial coma. This led to a reorganisation of the cabinet and the absence of President Pascal Couchepin from the United Nations General Assembly in New York City. On 10 December 2008, as the Member of the Federal Council that had not been its president for the longest time, Merz was elected President of the Confederation for 2009. In the Federal Assembly, the 66-year-old received 185 out of 209 valid votes. He succeeded Free Democratic Party colleague Pascal Couchepin. Doris Leuthard was elected as Vice President of the Confederation, succeeding Merz.

On 20 September 2010, a recording of Merz replying to a question about meat imports in the Federal Assembly became a viral video, drawing international attention. Merz convulsed with laughter when speaking, later saying that he found the dense bureaucratic language of the reply drafted for him by customs officials amusing. He was attempting to provide information about whether the sales of Bündnerfleisch in Switzerland were endangered by meat imports.

Works

 * Merz, Hans-Rudolf: Finanz- und Verwaltungsvermögen in öffentlich-rechtlicher und wirtschaftlicher Betrachtungsweise, unter besonderer Berücksichtigung der Staatsrechnungen der Kantone., St. Gallen 1971
 * Merz, Hans-Rudolf: Die aussergewöhnliche Führungspersönlichkeit: Essay über Elativität und elative Persönlichkeit., Grüsch 1987. ISBN 3-7253-0297-9
 * Merz, Hans-Rudolf: Der Landammann und weitere Erzählungen aus dem Appenzellerland, Herisau 1992. ISBN 3-85882-072-5

title: Hans-Rudolf Merz


text:
Talk:Baire space

Definition
I've seen that several authors define the Baire space to be NN, i.e. the irrationals. Might need a disambiguation page eventually. Revolver

Yes, I've seen that too (but only after I started this page!) For now, I'll just add the other definition, but we may well end up splitting them eventually. -- Toby Bartels 03:31, 11 Dec 2003 (UTC)

I'm concerned about the following example:

 * 1) Every space with an isolated point is a Baire space.  (Suppose x is an isolated point of X, and X is the countable union of nowhere dense subsets, then x is a member of a nowhere dense set, which is a contradiction, since the closure of any set containing x has interior at least equal to the singleton {x}, possibly more.)
 * 2) Consider the plane R2, and the subspace X which is the rational numbers Q union the isolated point {(0,1)}.  By the above, since X has an isolated point, it must be a Baire space.  Yet, if we take the singletons { {(q,0)} : q in Q}, then each of these is nowhere dense (they are closed, and has empty interior), so by one of the equivalent formulations of the definition, their union must have empty interior, which it clearly doesn't.  (This example should actually work for any non-Baire space by adding an isolated point to it.)

I think the definitions need to be checked closely, as this seems to be a counterexample. Revolver

I hope this is all straightened out now. I think this definition (every non-empty open set is non-meagre) is correct. In any case, I don't think it's immediately clear to a casual reader that all 4 conditions really are equivalent, and since the proofs are straightforward and short, this might not be a bad thing to have, as well. Revolver

I agree that your counterexample is sufficient to disqualify: as an equivalent definition. Would you agree to delete this definition? Missing the requirement that the nowhere dense set must contain no points isolated in the larger space, this erroneous definition has precipitated the misconception that "any space with an isolated point is a Baire space" as discussed below. A nowhere dense set with no points isolated in the larger space is just a special case of a set with empty interior. Howard McCay (talk) 06:52, 21 June 2013 (UTC)
 * The interior of every union of countably many closed nowhere dense sets is empty.

I think the main modern definition should be: the union of any countable collection of sets with empty interior has empty interior. I think the bottom equivalent definition should read: I do not see the need to require that the sets be closed for these definitions to work. Perhaps you can prove that if these definitions are given for closed sets only, then they can be extended to equivalent assertions applying to sets that are not necessarily closed. So maybe the closed set definitions are in this sense stronger. To me, putting unnecessary qualifications into a definition only makes the definition less clear. Howard McCay (talk) 06:52, 21 June 2013 (UTC)
 * Whenever the union of countably many subsets of X has an interior point, then one of the subsets must have an interior point.

Merged with Baire category theorem
I merged this page with Baire category theorem because I think both articles are too short and too closely related to be discussed on separate pages. I killed the purple boxes around the definitions and inserted some standard headings. Although the boxes looked nice I think the headings yield a better visual structure and standard heading like Definition and Examples provide the reader with faster access to relevant information. I tried to reorder and expand the material a bit to make it clearer but I am not sure I have succeeded. Anyway I intend to spend some more time working on this page the next few days. MathMartin 21:29, 27 Feb 2005 (UTC)

Splitting the set theory part into its own article
As of now, this article has to sections, one about Bair space in topology, and another one, much smaller, about Bair space in set theory. I wonder if it would be a good idea to split the second into Baire space (set theory) and put a link to it at the top of the article, like this:

 * ''For the set theory concept, see Bair space (set theory).

Would that be agreeable? Oleg Alexandrov

American v. British spelling
I understand the principle that the original author's spelling preferences should be kept, but I got to this page via a link from meager set, and then couldn't find "meager" in the page. So I've kept "meagre" as the primary spelling in deference to the principle, but added the Yank spellings as an aid to the wayfarer. --Trovatore 8 July 2005 22:45 (UTC)
 * See Manual of Style.  There's really no point in using both spellings - it's easy to see that "meager" is the American way of spelling "meagre" (or equally that "meagre" is the British way of spelling "meager"), and including both just clutters up the article.  The general principle is that if there is no reason to use one or the other (true in this case), the first editor's preference should be used.  http://en.wikipedia.org/w/index.php?title=Baire_space&direction=next&oldid=834287 uses "meagre", so we go with British spelling.  Hairy Dude 22:59, 15 January 2007 (UTC)

Question
An alternative definition of baire space: "Every intersection of countably many dense open sets is dense."

This seems unreasonable to me. Take for example the collection of sets $$ \ A_p=\mathbb Q + \frac{\pi}{p}$$, (where p is rational) the shift of the rationals by a non-rational number. This collection is pairwise disjoint, and therefore $$ \bigcap_p A_p=\emptyset $$ which is not dense. Am I wrong? --Yohai.bs 10:53, 20 July 2007 (UTC)

 * but those sets are "too small": they ain't open.  Mct mht 06:02, 24 July 2007 (UTC)

 * that is why openness is crucial (the intersection of the rationals and irrationals in $$R$$ is not dense but this does not imply that $$R$$ is not a Baire space).

Topology Expert (talk) 04:44, 31 October 2008 (UTC)

Any space with an isolated point is a Baire space
I just removed the sentence It should be pointed out that any space containing an isolated point is a Baire space, because an isolated point is its own interior. because it is false. It is true that an isolated point is its own interior, but that does not make the space a Baire space! If you take a non-Baire space (like the positive rational numbers) and add a single isolated point (like -1), then you will NOT get a Baire space! (The original space is an open subset of the new space with the additional point.  If the new space was a Baire space, the original one would also be one...) --131.234.106.197 (talk) 11:27, 19 May 2008 (UTC)

Very large, is it?
"Baire space is a topological space which, intuitively speaking, is very large" — really? A one-dimensional closed interval, is it "very large"? But wait; a finite set of points (even a single point), are they "very large"? What a strange intuition... Boris Tsirelson (talk) 11:02, 17 September 2013 (UTC)

 * I agree, it is not a great description. I rewrote the lead to be a bit more concrete. See if you find it more reasonable. --Mark viking (talk) 12:58, 17 September 2013 (UTC)

 * Better; but I still wonder: finite sets of points (even a single point), are they "very large"? Boris Tsirelson (talk) 20:40, 17 September 2013 (UTC)

title: Talk:Baire space