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Burra, South Australia

Burra is a pastoral centre and historic tourist town in the mid-north of South Australia. It lies east of the Clare Valley in the Bald Hills range, part of the northern Mount Lofty Ranges, and on Burra Creek. The town began as a single company mining township that, by 1851, was a set of townships (company, private and government-owned) collectively known as "The Burra". The Burra mines supplied 89% of South Australia's and 5% of the world's copper for 15 years, and the settlement has been credited (along with the mines at Kapunda) with saving the economy of the struggling new colony of South Australia. The Burra Burra Copper Mine was established in 1848 mining the copper deposit discovered in 1845. Miners and townspeople migrated to Burra primarily from Cornwall, Wales, Scotland and Germany. The mine first closed in 1877, briefly opened again early in the 20th century and for a last time from 1970 to 1981.

When the mine was exhausted and closed the population shrank dramatically and the townships, for the next 100 years, supported pastoral and agricultural activities. Today the town continues as a centre for its surrounding farming communities and, being one of the best-preserved towns of the Victorian era in Australia, as a historic tourist centre.

The Burra Charter, which outlines the best practice standard for cultural heritage management in Australia, is named for a conference held here in 1979 by Australia ICOMOS (International Council on Monuments and Sites) where the document was adopted.

Geology and geography
Burra is located within the Hundred of Kooringa a few kilometres inside Goyder's Line, near Burra, Baldina and Gum creeks. The lies within the Temperate Grassland of South Australia.

The main body of copper ore formed between two geological faults in broken dolomite rocks. The ore body was up to 70 metres (230 ft) wide and mainly consisted of green malachite and blue azurite veins and nodules amongst the host rock. The malachite and azurite were formed from copper sulphide minerals, by a process known as "secondary enrichment". This process took millions of years to convert the low grade copper sulphide ore, which was probably created 300 to 400 millions of years ago during the last period of vulcanism near Burra.

Etymology
The name applied to what is now the town of Burra has changed over time. The Burra Burra Copper Mine was named after the Burra Burra Creek that flows through the town. From at least 1851 the collection of townships near the mine became referred to as "The Burra". The town of Burra was officially formed in 1940 by a notice in the South Australian Government Gazette with the consolidation of the mostly culturally-based townships of Redruth, Aberdeen, New Aberdeen, Hampton, Copperhouse, Kooringa, Llwchwr, and Lostwithiel.

The name Burra Burra has been asserted to have come from numerous sources. As early as July 1843, when the locality was already a sheep outstation for pastoralist William Peter of Manoora, it was known as Burrow Creek. Despite that obvious (though misspelt) connection to the indigenous Ngadjuri people, a later theory persistently postulates that it comes from the Hindustani for 'great great', used by Indians shepherds working for another early pastoralist, James Stein, to refer to creek. The name could also have come from Stein's home country of Scotland or a number of Aboriginal languages. A so-called 'English Burra Burra' was discovered in 1851 in Devon in the Cornwall and West Devon Mining Landscape; possibly coincidentally several ancient placenames such as Burrator in Devon and Burraton in Cornwall occur nearby; also possible origins for the name. A Burra Burra mine is located in Tennessee and named after the Australian one.

Original inhabitants
The original inhabitants of the Burra area were the Ngadjuri Aboriginal people whose first Western contact was in 1839. The first European squatter in this region was William Peter, whose head station was Gum Creek near Manoora. Pastoralists grazed much of the Ngadjuri land from the 1840s and, although there was conflict, Ngadjuri people worked as shepherds and wool scourers, particularly once the area was emptied during the gold rushes of the 1850s. Their population was seriously depleted by introduced European diseases and they were reported to be extinct by 1878. Traces remain with rock art and burial sites in the area and some people able to claim Ngadjuri ancestry.

Discovery of copper
On 9 June 1845 William Streair bore samples of a rich copper ore into the office of Henry Ayers, secretary of the South Australian Mining Association (SAMA). Streair, a young shepherd in the employ of local pastoralist James Stein, had walked the 90 miles from Burra as did Thomas Pickett, a shepherd on a neighbouring property who made a further find. News of the copper this heralded was published on 21 June in Adelaide newspapers, and the site was soon named The Monster Mine.

Governor George Grey had amended land grant regulations forcing the hundred of Kooringa to be a 20000 acre rectangle, placing the two copper finds at opposite ends. Due to the £20,000 (sterling) price of the land it was divided in two, with each half sold to a different group and the division decided by lot. The surveyed area was named the Burra Creek Special Survey. It is 8 by, divided into two squares, 4 miles to a side. A group of wealthy capitalists (known as "the nobs") purchased the southern half of the division and a group of shopkeepers, merchants and SAMA (collectively known as "the snobs") the northern half.

The Burra Burra Mine was established by the snobs in their northern selection, the Princess Royal Mine by the nobs in their southern. In 1846, 347 acre just north of the division was sold to the Scottish Australian Investment Company for £5,550 where they established the Bon Accord Mine. Mining began on 29 September 1845 with the first gunpowder charge set off on the monster Burra Burra copper lode and by mid-1846, the Bon Accord Mining Company had also commenced operations.

Burra Burra or 'Monster Mine'

Until 1860 the mine was the largest metals mine in Australia. From 1845 to 1877 the mine produced approximately 50,000 tonnes of copper. The mine was reopened as a modern open cut in 1971, operating for a decade with 24,000 tonnes of copper extracted. The mine's Adelaide operation was run by Henry Ayers, secretary of SAMA, from its opening until the 1890s. Henry Roach was chief Captain, responsible for day-to-day operations, from 1847 to 1867. The investors had put up a total of £12,320 of which £10,000 was spent purchasing the land. The first dividend was paid on 24 June 1847 and by 1 December 1847 the mine had returned total dividends of £49,280. Over the mine's 32-year life, less than 100 shareholders received £826,586 in mining dividends. All mining dividends stopped after the mine closed in 1877, with the mine area sold in 1902 and the last property of SAMA in Kooringa sold in 1914. A final dividend was paid on 5 May 1916 and SAMA was wound up and closed.

Most of the copper was for sale to India as it was taking over a third of world copper supply in the mid-19th century. Due to the lack of smelting in South Australia, copper ore was initially shipped to Cornwall. The company purchased a Cornish beam engine which was the first in Australia when erected in 1848. Due to the uneconomic state of the mine, in 1868 a decision made to open cut the mine. Mining ceased underground, having reached a depth of 183 metres (600 ft) and open-cut operations starting in 1870 although, over the remaining life of the mine, small underground operations extracted more ore than the expensive open cut.

Over the life of the mine, Henry Ayers jealously preserved shareholder profits by ruthlessly controlling wages and expenses. In October 1846 this caused the first strike, of masons and bricklayers, with the company refusing to pay more than 8 shillings per day. With declining copper prices (from £91 per ton in 1845 to £87 in 1848) the company continually sought to reduce wages. In August 1847 the company enticed Thomas Burr to take over as general manager, he having resigned his post as Deputy Surveyor General of South Australia, but by September 1848 the unsatisfied company directors had sacked him. By 1848 the wages reached their lowest level, which precipitated the Burra miners' strike, being the first industrial strike in South Australia and earliest workers' strike of any consequence in Australia. The strike came and went numerous times, with miners not completely returning to work until January 1849.

By April 1848 the mine was employing 567 people and supporting a population of 1,500 in the township of Kooringa. Employment at the mine peaked at 1,208 in 1859 and declined continuously until the mine's closure in 1877. In November 1877 most of the remaining disposable equipment and stores were sold off and mining by SAMA ceased.

Bon Accord Mine
The Bon Accord Mining Company was formed on behalf of Scottish speculators, in the expectation that the Burra lode would extend under the properties boundary. No extension was found and, to recoup money, the townships of Aberdeen (1849) and New Aberdeen (1872) were formed on company land. Stoppage of pumping at the Burra Burra Mine in 1877 caused a rise in the water level in the neighbouring Bon Accord Mine forcing it to also close. Mining activity lasted from 1846 until 1849, was restarted in 1858 and finally ceased four years later with no orebody having been discovered. Many of the mine's buildings remain and are preserved by the National Trust of South Australia as a museum.

Princess Royal Mine
The Princess Royal Mine was never successful, and in June 1859 the Princess Royal Mining Company closed its doors. During its brief life the mine produced 468 LT of copper worth £6,500 from 888 LT of ore. The mine and surrounding 10000 acre of then pastoral land was auctioned on 24 April 1860.

Pastoral activity
From as early as 1843 shepherding had been common around Burra, with pastoral pioneers such as James Stein and William Peter being granted grazing rights for their flocks on unsurveyed land. Over the life of the Burra Mine, most food was brought in as there was no freehold offered by SAMA on the land and no adjoining hundreds were declared until 1860. Agriculture was delayed by the slow surveying of hundreds, as until these had been done there was no freehold or leasehold land but only grazing rights. As Burra lies almost on Goyder's 1865 line it is rated at the edge of marginal land for farming. After mining the town became a pastoral centre, and South Australia's main sheep trading centre until the mid-20th century. The Baldina Run, a major sheep station of 50 square miles some 10 miles east of Burra, near Kooringa, was established by Henry Ayers in 1851, leased by J and C. B. Fisher until 1862, then taken over by Alfred Barker, son-in-law of James Chambers.

Media
The Burra Record was a newspaper covering Burra and the mid-north eastern area. The Burra Record had begun life as the Northern Mail, the town's first publication, which was first published on 30 June 1876. After 26 weekly issues, in 1877, it was renamed to Burra News and Northern Mail, before being renamed again in July 1878. In 1977, it merged with the Review-Times to form the Review-Times-Record, which in turn became The Flinders News in 1989.

Another publication was the County Light Times, produced in the town from 3 March 1949 to 22 February 1951. Published by Harold Du Rieue, the newspaper's coverage included the districts of Riverton, Tarlee, Rhynie and Saddleworth.

Burra was also home to the Mid North Broadcaster, a publication released from 2006 to 2013. It was formed by the merger of struggling local newspapers, the Peterborough Times (2003–2006), the Burra Broadcaster (1991–2006), and the Eudunda Observer. It was owned by the Taylor group, with editorial control via the Murray Pioneer. Its distribution included the towns of Burra, Eudunda, Jamestown and Peterborough.

Development of the town
During a visit in October 1845 to Burra by Henry Ayers and the directors of SAMA the site of the township of Kooringa was chosen. George Strickland Kingston surveyed and laid out the township, completing it in April 1846, and named many of the streets after directors of SAMA. From the beginning the township was a company town, built at low cost and with insufficient housing, which forced many miners to dig makeshift homes. In the census of 1851 over a third of the population were living along the creek and the census compiler took time to note: "There are no houses, the dwellings being excavated in the banks of the Burra Creek." Largely due to the company nature of the settlement, development was slow, with the first bank not opening until 1859. Until the National Bank established the first branch in Kooringa, most exchange was either in the form of company scrip or at shops operating as money exchanges. All towns, except Kooringa, were built outside the mining lease but were still close to the mine as it was at the northern edge of the lease. The formation of the townships was forced by the refusal of SAMA to grant any freeholds within Kooringa, so miners began moving into other townships from the end of 1849. During their early lives, each of the townships largely had their own hotels, churches, post offices, schools, and shops and identity. In 1851 the gold rush near Bathurst, New South Wales, emptied the town of many miners. Whole families, government officials and other townspeople left for the gold fields and by 1854 the town appeared largely deserted. The number of townships increased dramatically as a result of an 1858 proposal to extend a railway line from Gawler. When the railway failed to be built most of the new townships failed and, in 1876, the remaining townships formed the Corporation of Burra.

In September 1846 the townships had their first police force with the movement of four constables from Julia Creek to the south into temporary accommodation provided by SAMA. Permanent lockup cells and stables were completed in Redruth mid-1847. In September that year, William Lang was appointed resident magistrate and coroner for the Murray District and initially housed in a company cottage in Kooringa. The first hotel was a temporary wooden structure erected at the entrance to the township of Kooringa in mid-1846, and the first permanent hotel was the Burra Hotel (opened 25 September 1847) built by William Paxton, a SAMA director and original owner of Ayers House. The Burra Hotel became the town's first public hospital in 1878 and was demolished in 1968.

Burra's first parliamentary representative was George Strickland "Paddy" Kingston who was elected in 1851 to the first legislative council as member for Burra and Clare, and for the same area to the house of assembly in its first parliament of 1857.

Piped water was supplied from 1884 from the flooded and abandoned Bon Accord Mine with water reaching 100 houses by 1885. This was the primary source for Burra until 1966 when it was replaced with water piped from the Murray River. The Burra received its first supply of electricity on 27 March 1924 from the newly formed Burra electric supply company.

The historic Burra neighbourhoods of Kooringa, Llwchwr, Aberdeen, New Aberdeen, and Graham ceased to be separately recognised and were included as part of Burra township proper in July 1940. Redruth was renamed "Burra North" at that time; it would eventually be merged with Burra as well.

Burra's population has declined from a peak of 5,000 in 1851 to a present figure of approximately 1,000. The dramatic decrease at the end of mining inhibited expansion and helped preserve many of the original buildings and houses. The District Council of Burra was proclaimed in 1872, the Town Corporation in 1876 and in 1969 the District Council and Town Corporation were amalgamated.

Redruth
Redruth was a government township formed in 1850 to break SAMA's monopoly. It is named after Redruth in Cornwall and its streets are named after Cornish mining towns. The township was the site of all original government buildings (courthouse, gaol and police station). The courthouse was erected in 1857, and Redruth Gaol, built in 1856, was the first country gaol in South Australia. From 1897 to 1922, the gaol was used as a girls' reformatory. SAMA delayed building in Redruth when they bought 77 of the 120 lots on offer at the initial land auction, paying almost 20 times the overall reserve price.

Kooringa
Kooringa was the first company township in Australia and, until the closure of the mine, was maintained as a strictly company-run town. The township's name is derived from the Aboriginal word kuri-ngga meaning either in the circle or locality of the sheoak. During the life of the Burra Burra Mine, the township was widely reported as shabby, rundown and poorly maintained with the inhabitants having little incentive to maintain their rented properties. Kooringa is still the main section of the town and is known as Burra South.

Llwchwr
Llwchwr, sometimes spelled Llychwr, was built by the Patent Copper Company (later the English and Australian Copper Company) to avoid the need to ship all of the ore to Wales. The streets are named after those in Llwchwr, Wales and other nearby villages. In May 1848, the company had imported from Swansea the entire smelting works comprising men, materials, tools, staff and families. Smelting was reported to be in operation by May 1849.

Aberdeen and New Aberdeen
In 1846 a group of speculators from Scotland formed the Bon Accord Mining Company, purchasing a section of land on the northern boundary of the special survey, hoping that the ore body extended under the boundary. Due to the lack of success in mining company, land near the mine was subdivided in 1849 forming Aberdeen (named after the east coastal city of Aberdeen in Scotland), with the company seeking to recoup some of their investment. Streets were named to honour directors of the Bon Accord Mining Company and the retention of mineral rights by the company prevented SAMA from acquiring the land, as they had in Redruth. New Aberdeen was subdivided after 1872 arrival of the railway line from Kapunda, and most of the early buildings in the two townships were constructed in the three years following.

Railway
The broadgauge railway eventually went through Burra to reach a break of gauge station further north at Terowie.

Burra railway station is 1555 ft above sea level and 112 mi from Adelaide. It was erected in 1883, replacing the original building. Regular passenger services ended at the end of 1986, with the last passenger train being an ARHS steam train on 19 September 1992. The last light engines ran to Burra in 2004 with the line being formally closed. After falling into disrepair, the station building has been renovated for use as a visitor centre and B&B.

Other townships
The townships of Copperhouse, Hampton and Nelson were not included in the 1940 proclamation forming the town of Burra, as they had become ghost towns. Other townships that either never succeeded or had been abandoned by 1940 were Princesstown, Lostwithiel, Westbury, Roachtown, Yarwood, Millertown, Warrapoota and Clonmel.

Burra today
Burra today is an important regional centre for surrounding farming communities and a historic tourist destination. From its 1994 declaration as a State Heritage Town, tourism has grown to an estimate of 41,000 visitors in 2000. While many visitors are day-trippers and are from Adelaide, over 40% of the visitors come from outside South Australia and over 50% stay overnight.

The town and mine are both well preserved with many original buildings, the water filled open cut mine, well-preserved mining buildings and a pump engine house which today houses a museum. Several chimneys from the mining industry have survived and a tourist trail showcases the old Redruth Gaol, miners' dugout cottages in the creek bank, a row of miners' cottages built in 1850, the cellars of the demolished Unicorn Brewery and other historic places. Burra is listed on the Register of the National Estate and many buildings are on the List of State Heritage Items. The town is publicly claimed to be the "Merino capital of the world".

title: Burra, South Australia


text: Category:Counts of Flanders

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

title: Category:Counts of Flanders


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Kolinda Grabar-Kitarović

Kolinda Grabar-Kitarović (born 29 April 1968) is a Croatian politician and diplomat who served as President of Croatia from 2015 to 2020. She was the first woman to be elected to the office since the first multi-party elections in 1990 and independence from Yugoslavia in 1991. At 46 years of age, she also became the youngest person to assume the presidency.

Before her election as President of Croatia, Grabar-Kitarović held a number of governmental and diplomatic posts. She was minister of European Affairs from 2003 to 2005, the first female minister of Foreign Affairs and European Integration from 2005 to 2008, Croatian ambassador to the United States from 2008 to 2011 and assistant secretary general for public diplomacy at NATO under Secretaries General Anders Fogh Rasmussen and Jens Stoltenberg from 2011 to 2014.

She is a recipient of the Fulbright Lifetime Achievement Award and a number of national and international awards, decorations, honorary doctorates and honorary citizenships.

Grabar-Kitarović was a member of the conservative Croatian Democratic Union party from 1993 to 2015 and was also one of three Croatian members of the Trilateral Commission, but she was required to resign both positions upon taking office as president in 2015, as Croatian presidents are not permitted to hold other political positions or party membership while in office. As president, she launched the Three Seas Initiative in 2015, together with Polish President Andrzej Duda. In 2017, Forbes magazine listed Grabar-Kitarović as the world's 39th most powerful woman.

In 2020 she was elected Croatia's representative in the International Olympic Committee.

Early life and education
Kolinda Grabar was born on 29 April 1968 in Rijeka, Croatia, then part of Yugoslavia, to Dubravka (b. 1947) and Branko Grabar (b. 1944). She was raised mainly in her parents' village of Lopača, just north of Rijeka, where the family owned a butcher shop and a ranch. As a high school student, she entered a student exchange program and at 17 moved to Los Alamos, New Mexico, subsequently graduating from Los Alamos High School in 1986.

Upon her return to Yugoslavia, she enrolled at the Faculty of Humanities and Social Sciences, University of Zagreb, graduating in 1993 with a Bachelor of Arts in English and Spanish languages and literature. From 1995 to 1996, she attended the Diploma Course at the Diplomatic Academy of Vienna. In 2000 she obtained a master's degree in international relations from the Faculty of Political Science at the University of Zagreb.

In 2002–2003, she attended George Washington University's Elliott School of International Affairs as a Fulbright scholar. She also received a Luksic Fellowship at the Harvard Kennedy School at Harvard University and was a visiting scholar at the School of Advanced International Studies at Johns Hopkins University.

In December 2015, Grabar-Kitarović began her doctoral studies in international relations at the Zagreb Faculty of Political Science.

Career
In 1992, Grabar-Kitarović became an advisor to the international cooperation department of the Ministry of Science and Technology. In 1993 she joined the Croatian Democratic Union (HDZ). In the same year she transferred to the Foreign ministry, becoming an advisor. She became the head of the North American department of the Foreign ministry in 1995 and held that post until 1997. That year she began to work at the Croatian embassy in Canada as a diplomatic councilor until October 1998, and then as a minister-councilor.

When Social Democratic Party of Croatia (SDP) came to power after 2000 elections Tonino Picula became minister of Foreign Affairs. After taking office he immediately started to remove politically appointed staff that had been appointed by the Croatian Democratic Union (HDZ) to high-ranking diplomatic positions. Grabar-Kitarović was ordered to return to Croatia from Canada within next six weeks, which she at first refused to do because she was pregnant and had already made plans to give birth in Canada, however she eventually decided to return after being strongly pressured by the ministry to do so. During her stay in the hospital, she applied for Fulbright scholarship for studying international relations and security policy. She eventually moved to the United States and enrolled at George Washington University. After graduating, she returned to Croatia and continued to live in Rijeka.

Two years later, she was elected to the Croatian Parliament from the seventh electoral district as a member of the Croatian Democratic Union in the 2003 parliamentary elections. With the formation of the new government led by HDZ chairman Ivo Sanader she became Minister of European integration, which entailed the commencement of negotiations regarding Croatia's accession to the European Union.

After the separate ministries of Foreign Affairs and European Integration were merged in 2005 Grabar-Kitarović was nominated to become minister of Foreign Affairs and European Integration. She was confirmed by the Parliament and sworn in on 17 February 2005. Her main task as foreign minister was to guide Croatia into the European Union and NATO. On 18 January 2005, she became head of the State Delegation for Negotiations on the Croatian accession to the European Union. Furthermore, on 28 November 2005 she was elected by the international community to preside over the Anti-Personnel Mine Ban Convention's Sixth Meeting of the States Parties, or Ottawa Treaty, held that year in Zagreb. Grabar-Kitarović was the first woman to be named president of the Ottawa Treaty.

Following the HDZ's victory in the 2007 parliamentary election and the subsequent formation of the Second Sanader Cabinet, she was reappointed as foreign minister, but was suddenly removed from the position on 12 January 2008. The exact reason for her removal is not known. Gordan Jandroković succeeded her.

On March 8, 2008, while the President of Croatia was Stjepan Mesić, she became the Croatian ambassador to the United States, where she replaced Neven Jurica. She served as ambassador until 4 July 2011.

On October 24, 2008, Grabar-Kitarović joined President George W. Bush and NATO Secretary General Jaap De Hoop Scheffer during the signing of NATO accession protocols in the East Room of the White House, in support of the nations of Albania and Croatia joining the NATO alliance.

On May 6, 2010, the Croatian Embassy held a reception to celebrate women diplomats at the Croatian Embassy, which was attended by ambassadors to the U.S. from Croatia, India, Liechtenstein, Trinidad and Tobago, Grenada, Senegal, and Antigua and Barbuda. The event was opened by Grabar-Kitarović by discussing the importance of taking small steps when it comes to mentoring.

In 2010 Croatian Embassy in Washington, DC discovered that Grabar-Kitarović's husband, Jakov, had been continually filmed while using an official embassy car. A member of the embassy's security staff had followed and filmed Kitarović, recording footage that was posted on YouTube. As a result, Foreign Minister Gordan Jandroković launched an internal investigation into the unauthorized filming of members of the diplomatic staff and their families by a member of the embassy's security staff. A member of the embassy's security staff who had filmed her family was fired.

In 2011, Grabar-Kitarović was appointed Assistant Secretary General for Public Diplomacy at NATO, the first women to hold the position. Her task was to take care of the "communication strategy" and to "bring NATO closer to the common people". Her colleagues at NATO often referred to her as SWAMBO (She Who Must Be Obeyed). She served until 2 October 2014.

She was invited to join the Trilateral Commission and became an official member in April 2013.

Support for 2014–2016 Croatian war veterans tent protest
During her presidential candidacy, Kolinda Grabar-Kitarović supported protesting war veterans, despite the fact that the group of protesters near the central tent blocked the traffic and brought bottles of gasoline on Savska street which they apparently threatened to ignite if the police refused to back off. This support for war veterans, regardless threats of violence, was considered an unacceptable populist posture in order to gain the support of more of the right-leaning electorate in the upcoming presidential election.

2014–15 presidential candidacy
Croatian daily newspaper Jutarnji List published an article in September 2012 stating that Grabar-Kitarović was being considered as a possible candidate for the 2014–15 Croatian presidential election by the Croatian Democratic Union (HDZ). It was confirmed in mid-2014 that she was to become the party's official candidate, going up against incumbent Ivo Josipović and newcomers Ivan Vilibor Sinčić and Milan Kujundžić. In the first round of election in December 2014 Grabar-Kitarović won 37.2% of the vote, second to Josipović who received 38.5%, while Sinčić and Kujundžić won 16.4% and 6.3% of the vote respectively. Since no candidate received more than 50% of the vote, a run-off election was scheduled between the top two candidates, Josipović and Grabar-Kitarović, in two weeks time.

Grabar-Kitarović contested the presidential election held in December 2014 and January 2015 as the only female candidate (out of four in total), finishing as the runner-up in the first round and thereafter proceeding to narrowly defeat incumbent president Ivo Josipović in the second round (by a margin of 1.48%). Furthermore, as the country had previously also had a female prime minister, Jadranka Kosor, from 2009 until 2011, Grabar-Kitarović's election as president led to Croatia's inclusion in a small group of parliamentary republics which have had both a female head of state and head of government.

The run-off took place on 11 January 2015, with Grabar-Kitarović winning 50.7% of the vote. She thereby became Croatia's first female post-independence head of state and the country's first conservative president in 15 years. She was ceremonially sworn into office on 15 February, and assumed office officially at midnight on 19 February 2015.

Upon election, Grabar-Kitarović became the first woman in Europe to defeat an incumbent president running for reelection, as well as the second woman in the world to do so, after Violeta Chamorro of Nicaragua in 1990. She is also the first candidate of any gender to defeat an incumbent Croatian president. In addition, Grabar-Kitarović is the only presidential candidate to date to have won a Croatian presidential election without having won the most votes in the first round of elections, as she lost it by 1.24% or 21,000 votes. Furthermore, the 1.114 million votes she received in the second round is the lowest number of votes for any winning candidate in a presidential election in Croatia and the 1.48% victory margin against Josipović is the smallest in any such election to date.

Presidency (2015–2020)
Less than nine months into Grabar-Kitarović's term the European migrant crisis began to escalate with large numbers of migrants entering Greece and Macedonia and crossing from Serbia into Hungary, with the latter beginning the construction of a fence on its southern border as a result. In September 2015, after Hungary constructed a fence and closed its border with Serbia, the flow of migrants was redirected towards Croatia, causing over 21,000 migrants to enter the country by 19 September, with the number rising to 39,000 immigrants, while 32,000 migrants exited Croatia, leaving through Slovenia and Hungary. She appointed Andrija Hebrang her commissioner for the refugee crisis.

With the parliament expected to dissolve by 25 September, Grabar-Kitarović called parliamentary elections for 8 November 2015. They proved inconclusive and negotiations on forming a government lasted for 76 days. Grabar-Kitarović had previously announced on 22 December 2015 that if there was no agreement on a possible Prime Minister-designate in the next 24 hours, she would call for an early election and name a non-partisan transitional government (which would have reportedly been headed by Damir Vanđelić), thereby putting intense pressure on the political parties involved in the negotiations regarding the formation of the new government, to find a solution. The crisis finally ended on 23 December 2015 when Grabar-Kitarović gave the 30-day mandate to form a government to the non-partisan Croatian-Canadian businessman Tihomir Orešković, who had been selected by HDZ and MOST only hours before the expiration of the President's delegated time frame for the naming of a Prime-Minister-designate.

On 24 August 2015, Grabar-Kitarović was, as Armed Forces Commander-in-Chief, presented with a petition for the introduction of a salute Za dom spremni to the official use in the Croatian Armed Forces. She immediately rejected the petition, calling it "frivolous, unacceptable and provocative". She called the salute a "Croatian historical greeting" that was "compromised and unacceptable". Following a backlash from some historians that the salute was not historical, Grabar-Kitarović admitted that she was wrong in that part of the statement.

On 29 September 2015, at the initiative of Grabar-Kitarović the Atlantic Council co-hosted an informal high-level Adriatic-Baltic-Black Sea Leaders' Meeting in New York City which would later grow to Three Seas Initiative. The Initiative was officially formed in 2016 and held its first summit in Dubrovnik, Croatia, on 25–26 August 2016.

On 11 April 2016, after meeting with Nicolas Dean, the special envoy for Holocaust of the United States Department of State, Grabar-Kitarović stated that the "Independent State of Croatia (NDH) was least independent and was least protecting the interests of the Croatian people". Adding that the "Ustaše regime was criminal regime", that "anti-fascism is in the foundation of the Croatian Constitution" and that the "modern Croatian state has grown on the foundations of the Croatian War of Independence." In May 2016, Grabar-Kitarović visited Tehran on the invitation of Iranian President Hassan Rouhani. Rouhani called on Croatia to be the gateway to Iran's ties with Europe. The two presidents reaffirmed the traditionally good relations between their countries and signed an agreement on economic cooperation.

Grabar-Kitarović expressed her condolences to Slobodan Praljak's family after he committed suicide in The Hague where he was facing trial, calling him "a man who preferred to give his life, rather than to live, having been convicted of crimes he firmly believed he had not committed", adding that "his act struck deeply at the heart of the Croatian people and left the International Criminal Tribunal for the Former Yugoslavia with the weight of eternal doubt about the accomplishment of its tasks".

In a speech held at the ceremony at which Grabar-Kitarović was named honorary citizen of Buenos Aires in March 2018, she stated that "after World War II, many Croats found a space of freedom in Argentina where they could testify to their patriotism and express their justified demands for the freedom of the Croatian people and homeland." Following the end of the war and the establishment of a communist regime, about 20,000 Croats, mostly political emigrants, moved to Argentina. As some among them were members of the Ustaše movement, her statement was interpreted by some, including Efraim Zuroff of the Simon Wiesenthal Center, as support for them. In a press release, Grabar-Kitarović rejected what she described as "malicious interpretations" of her statement.

During the 2018 FIFA World Cup, held in Russia, Grabar-Kitarović attended the quarter-final and final matches, wearing the colors of the national flag in support of the national team, which ultimately ended up as tournament runners-up. According to the analytics company Mediatoolkit, she "emerged as her country’s star of the tournament" with "25% more focus on her in news stories about the final than any of the players on the pitch", as she "travelled to Russia at her own expense in economy class and often watched from the non-VIP stands". Commenting on the appearance of Croatian singer Marko Perković at the celebration, Grabar-Kitarović stated that she “never heard” such songs nor “seen any evidence that they exist”, was "very fond" of some of his songs and that she did not see any evidence for the controversies associated to him, claiming his songs are "good for national unity". She condemned all totalitarian regimes, including nazism, fascism, and communism.

Grabar-Kitarović was awarded Fulbright Association's 2019 Lifetime Achievement Award for her "remarkable, contributions as a leader, diplomat, and public servant".

2019–20 Croatian presidential election
In August 2019, during the Victory Day celebrations in Knin, Grabar-Kitarović informally hinted that she would be seeking reelection to a second and final 5-year term as president in the upcoming election, and formally confirmed this several days later in an interview for the right-wing publication Hrvatski tjednik (Croatian Weekly). Prime Minister and HDZ President Andrej Plenković announced that the HDZ would support her bid for a second term. On 2 October 2019, Grabar-Kitarović formally announced her bid for re-election with the campaign slogan "Because I believe in Croatia". She thus proceeded to face 10 other candidates in the first round on 22 December 2019, with her main challengers being former Social Democratic Prime Minister Zoran Milanović and conservative folk musician and former Member of Parliament Miroslav Škoro. Zoran Milanović won a plurality of 29.55% of the vote, ahead of Grabar-Kitarović, who received 26.65% of the vote, while Miroslav Škoro attracted the support of 24.45% of voters. Therefore, this election marked the first time in Croatian history that the incumbent president did not receive the highest number of votes in the first round. Grabar-Kitarović only managed to defeat Škoro by a margin of 2.2% of the vote, and therefore narrowly proceeded to the run-off against Milanović. Also, Grabar-Kitarović attained both the lowest number of votes (507,626) and the lowest percentage of votes of any sitting Croatian president competing in either of the two rounds of elections. Furthermore, Milanović attained both the lowest number of votes (562,779) and the lowest percentage of the vote of any winning candidate in the first round of a presidential election.

A run-off election took place between Milanović and Grabar-Kitarović on 5 January 2020. She was eventually defeated in her bid for reelection by Milanović, who won 52.66% of the vote, while Grabar-Kitarović, who had tried to unite a fractured right wing, garnered 47.3%. The turnout was about 55%. She is thus the second President of Croatia to not win a second term, after her predecessor Ivo Josipović. Grabar-Kitarović left the presidency on 18 February 2020, when she handed over the office to Milanović, who thus became the 5th President of Croatia since its independence.

Political positions
Grabar-Kitarović declared herself a "modern conservative" during the 2014–15 presidential election. Her political positions have mostly been described as conservative in the media. Agence France-Presse wrote that Grabar-Kitarović represents moderates within her party. Some observers describe her actions as populist,  or nationalist.

On the societal level, she moderates the positions of her party, traditionally reticent towards homosexuality and abortion. On the issue of same-sex marriage, Grabar-Kitarović expressed her support for the Life Partnership Act, which enabled same-sex couples to enjoy rights equal to heterosexual married couples except in adoption, as good compromise.

Grabar-Kitarović considers that the prohibition of abortion would not solve anything, and stresses that attention should be paid to education in order to prevent unwanted pregnancies. Grabar-Kitarović criticized the hard process of adoption and stated that "the whole system has to be reformed so that through education and social measures it enables every woman to give birth to a child, and that mother and the child can eventually be taken care of in an appropriate manner."

Grabar-Kitarović has spoken in support of green initiatives along with the dangers of climate change for the environment and global security. In 2016, she signed the Paris Agreement at UN Headquarters in New York City. During another speech at the UN, she stated that climate change was a "powerful weapon of mass destruction."

International Olympic Committee
In 2020, she was elected to the International Olympic Committee as the 5th representative of Croatia in this body and first female member in this position.

Personal life
Grabar-Kitarović has been married to Jakov Kitarović since 1996 and they have two children: Katarina (born on 23 April 2001), a figure skater and Croatia's national junior champion; and Luka (born c. 2003).

Grabar-Kitarović is a practising Roman Catholic. In an interview for Croatian Catholic Network, she stated that she regularly attends Mass and prays the Rosary.

In an interview for Narodni radio, Grabar-Kitarović stated that her favorite singer was Croatian nationalist singer Marko Perković.

She speaks Croatian, English, Spanish and Portuguese fluently and has basic understanding of German, French and Italian.

On 30 December 2020, Grabar-Kitarović made a cameo appearance in the Croatian telenovela Dar mar, playing herself.

title: Kolinda Grabar-Kitarović


text:
Khor

Khor (also Hurru, Kharu) is the second, later name used by ancient Egyptians after using Retjenu in designating the wider Syrian region, where the Semitic-speaking Canaanites lived. It was long an outpost of ancient Egypt, and is explicitly mentioned in the Great Hymn to the Aten as a geographic region, along with the kingdoms of Kush and Egypt. Based on the Amarna letters, it is plausible that Khor is a Middle Egyptian reference to Canaan.

This word spelled as Hurru or Kharru is also used on the Merneptah Stele. In this inscription,

"Hatti and Hurru stand for the whole region of Syro-Palestine; Canaan and Israel represent smaller units within the area, and Gezer, Ashkelon, and Yanoam are three cities within the region.'"

Pharaoh Taharqa claimed to conquer this territory as attested by the "list of conquered Asiatic principalities" from the Mut temple at Karnak, as well as in Sanam temple inscriptions. Taharqa disputed this region with Sennacherib of Assyria.

The Egyption Story of Wenamun refers to a location named Kharu. According to Alessandra Nibbi, the expression "the great ym of Kharu" is often connected to the Mediterranean sea. But she was trying to reinterpret this and other associated geographical names and to tie them to other locations.

title: Khor


text:
Talk:NFL on CBS

Untitled
This isn't quite true. It shows AFC away games, but they may be against NFC opponents. RickK 08:14, Feb 20, 2005 (UTC)

Lowell W. Perry?
I'm worrking on Lowell W. Perry and just read this: http://www.infoplease.com/ipa/A0880677.html about a brief(?) broadcasting career. Anyone ever heard of him in the world of sports broadcasting? Charles (Kznf) 19:37, 12 February 2007 (UTC)

hotmail was clicking the word at the computer

your tpye the word........

I love the NFL on CBS. I can't wait until Sunday again! —Preceding unsigned comment added by 99.235.220.122 (talk) 04:05, 14 January 2009 (UTC)

Digital on-screen graphics
This article does a great job explaining the history of the digital on-screen graphics that CBS has had over the years. However, we have no visual examples to show what these graphics look like. Without visual examples, this section is pointless. Low resolution examples need to be uploaded using File Upload Wizard and shown in this section to ensure accuracy of what the graphics look like. Thank you.

Albino Geronimo 00:18, 18 February 2014 (UTC)
 * Sorry, but I think it's trivia and fancruft. ViperSnake151   Talk  01:12, 14 December 2014 (UTC)

Schedules
Are the time slots in the schedules necessary? I know we don't usually put time slots on here per WP:NOTTVGUIDE, but I'm questioning this one. I think the tables can be here without having the time slots on here, as I don't see them as important information, but yet again I can see them being helpful. All that really needs to be there is the Date, Teams, and Announcers. I didn't want to remove the column without discussing it first. What are others' thoughts on this?  Corky  |  Chat?  21:13, 27 March 2015 (UTC)
 * It is also on NFL on NBC.  Corky  |  Chat?  22:57, 28 March 2015 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 1 one external link on NFL on CBS. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20061005034505/http://blogs.kansascity.com:80/tvbarn/2006/01/why_cbs_sports_.html to http://blogs.kansascity.com/tvbarn/2006/01/why_cbs_sports_.html

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New logo?
Last Sunday, CBS Sports unveiled their new logo (stylized as 👁CBS | NFL). Is there a version somebody could find in order to update this page? Jimania16 (talk) 17:01, 1 September 2021 (UTC)

OR tag
The entire on-screen graphics section is unsourced, and seems to be original research. Is it even worthy of inclusion? It seems like trivia. --fuzzy510 (talk) 05:17, 17 January 2022 (UTC)

title: Talk:NFL on CBS


text:
Talk:Claiborne Fox Jackson

Untitled
I'm adding information I obtained from http://www.nps.gov/peri/jackson.htm. The content there was created by US Government employees as part of their official duties, so is Public domain. Kenj0418 08:15, Feb 20, 2005 (UTC)

I'm doing a major revision using Thomas Snead's The Fight for Missouri as a primary source for correcting some massive errors about the governor's statements and positions as well as events. Unfortunatley, I lost two massive edits and will have to start again.

There is some heavily Southern perspective (well beyond that of Snead who was a period secessionist and worked for Jackson) of events in the previous draft that I will be addressing to neutralize the article, and correct a mangled timeline, for instance:

1. Contrary to the original wording the St. Louis Arsenal was a United States Arsenal. There was therefore no need for U.S. officers to "seize" their own arsenal as it was already in their hands. Lyon did make it more secure, despite the objections of his superiors in St. Louis.

2. Analysis by Dr. Randy R. McGuire indicates that the number of weapons is overstated by many contemporaries and as stated here. See http://www.civilwarstlouis.com/arsenal/index.htm

3. The arms shipment by the CSA to the militia at Camp Jackson was not "alleged." There is correspondence from both sides confirming this, and the arms were actually seized by Lyon's men. (April 17th Jackson's request, April 23rd Davis' response.)

4. The MSG was still referred to as "militia" until Jackson's new Military Bill was passed after the St. Louis Riot/Massacre/Camp Jackson Affair. The organization was renamed by the legislation.

5. Although the great majority of the Union volunteers involved in the Camp Jackson affair were German, not all were (this is evident from the muster rolls and census data.)

6. The riot started before any shooting by the soldiers occurred. The previous wording makes it sound as if the soldiers just merrily began killing militia and civilians for sport and a riot resulted.

7. Price was not offered his commission until May 12.

8. The Price-Harney meeting occurred on May 20.

9. Again contrary to original tone and wording of the article, the State Convention (under Price, no less) had orginially rejected secession on March 9, 1861 by 98 to 1. Red Harvest (talk) 04:36, 27 November 2007 (UTC)
 * 1. Lyon seized it from another US officer who had not given him access to it, and he took it without authority from BG Harney. Seizure is the right word.  3-8, I concur, altho' one could argue on 6 when the "disturbance" became a "riot", I find such things not worth quibbling over. 138.162.128.52 (talk) 12:48, 15 April 2011 (UTC)

Bias
This article seems to be very pro-Confederate and at times seems to conflict with information elsewhere in Wikipedia. The vote to secede ignores whether the vote was legal to begin with. This article also lacks sources for material, except, apparently, for the location of his burial.75.88.41.182 (talk) 03:34, 28 January 2009 (UTC)

I'm surprised to see not a single reference to Jackson's involvement in Bleeding Kansas.--jdege (talk) 01:34, 13 April 2010 (UTC)

Citing sources
The above lists several sources that have not been cited in the article. They should be checked against the existing content of the article and wp:inline citations added as applicable. Additional material is available from this query against the University of Missouri Digital Collections. Follow the "Result details" links for the match pages, then the specific page numbers listed for the text that matched. LeadSongDog come howl!  03:47, 24 June 2010 (UTC)

The "Political offices" section
This section is biased in that it accepts Lyon's de facto, but no de jure, "firing" (admittedly a poor choice of words on my part) of Gov Jackson in 1861. The truth is that Gov Jackson was governor of the US state of Missouri from January 3, 1861 to July 23, 1861 (by Lyon's reckoning) and was succeeded by Gamble in that role. He was also governor of the Confederate state of Missouri from October 31 (or arguably November 28, 1861, when the Confederacy ratified the vote and admitted Missouri as their 12th state) until his death on December 6, 1862, and was succeeded by Thomas Caute Reynolds. Admittedly, this leaves his status unclear between July 23, 1861, and October 31, 1861, when Missouri had no yet seceded but he had been driven from Jefferson City by Lyon. (The period of "armed neutrality". The best argument, IMHO, is that Missouri had two governors during this time -- Jackson and Gamble, one elected and one appointed. My recommendation is that the box be split to show this. 138.162.128.52 (talk) 12:45, 15 April 2011 (UTC)

Timeline is jumbled
The timeline has been jumbled in the article. His ouster by the Missouri Constitutional Convention's executive committee has been placed in the same period as the original convention...it was not. Will need to rearrange/alter several sections. Red Harvest (talk) 05:18, 5 July 2014 (UTC)

title: Talk:Claiborne Fox Jackson


text:
Wikipedia:Wikipedia Signpost/2005-02-21/Wired feature

The March 2005 issue of Wired Magazine hit newsstands last week with a lengthy article about Jimmy Wales and Wikipedia. The magazine also announced the winners of its Rave Awards, but Wales, who had been nominated, was not among them.

The article, written by Daniel H. Pink, was entitled "The Book Stops Here", and a line on the magazine cover billed it as "Wikipedia: The self-organizing library of the future". It mixes brief sketches (both verbal and visual) of individual Wikipedians with a discussion of the project's history, objectives, and challenges.

Pink discusses a variety of Wikipedia phenomena in the article. He describes Wikipediholism as a four-step process: a chance encounter with the site, followed by curiosity, experimentation, and finally addiction. Also considered is the "power pyramid" of Wikipedians, with "God-King" Jimbo at the top, which he paints as an evolutionary response to the problems caused by "those who have difficulty playing well with others."

Also included is an analysis of how Wikipedia compares to other models for creating an encyclopedia. Pink slots in Wikipedia as a new model, following the classical model in which encyclopedias are written by great minds, and the more managed and organized system used by Encyclopædia Britannica and other modern examples. As he puts it, this model creates something "alive" rather than something "finished". He wraps up the article with some passages quoted from former Britannica editor Charles Van Doren, who says, "the ideal encyclopedia should be radical."

Part of Pink's research for the article was conducted at the Wikipedia Meetup in New York City on 12 December of last year. Out of the Wikipedians who were specifically mentioned in the article, four besides Wales attended the meetup — Danny, Ram-Man, Raul654, and Angela. Pink did feature a few additional users, including Carptrash, Bryan Derksen, Kingturtle, and Lord Emsworth, and also contacted Larry Sanger for his input.

Commenting on the piece, Sj gave it a generally positive review but said, "The one glaring omission in the article is an acknowledgement of the project's unparalleled multilinguality." Only one sentence mentions it, and its initial words, "Tack on... [other languages]", reflect how the subject is being treated in the article. One can also observe that of the Wikipedians mentioned, all are residents of North America but for Angela (along with Solitude and Ahoerstemeier, who get the briefest of mentions for reverting vandalism to Islam back on 17 November 2004 - though Pink doesn't specify the date).

Rave Award winners revealed
Also included in this issue were the winners of Wired's annual Rave Awards. Wales had been nominated for one of these awards in the Tech Innovator category (see archived story), but did not end up getting it. The winner of the award for the category was Mark Fletcher, CEO of the news aggregator website Bloglines. Apparently, not having a Wikipedia article about himself or his company was not an insurmountable handicap.

The nominees in this category also changed midway through the process, as Scott Maccabe, vice president and general manager of Toshiba's Storage Device Division, replaced Bill Healy, a senior vice president of product strategy and marketing at Hitachi Global Storage Technology, as the person associated with the microdrive. It seems that perhaps Wired decided it made little sense to give a marketing guy credit for innovation in technology.


text:
User talk:Fipe

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Research survey invitation
Greetings Fipe-

My name is Randall Livingstone, and I am a doctoral student at the University of Oregon, studying digital media and online community. I am posting to invite you to participate in my research study exploring the work of Wikipedia editors who are members of WikiProject: Countering Systemic Bias. The online survey should take 20 to 25 minutes to complete and can be found here:

https://oregon.qualtrics.com/SE/?SID=SV_cSHzuwaQovaZ6ss

Your responses will help online communication researchers like me to better understand the collaborations, challenges, and purposeful work of Wikipedia editors like you. In addition, at the end of the survey you will have the opportunity to express your interest in a follow-up online interview with the researcher.

This research project has been reviewed and approved by the Wikimedia Research Committee as well as the Office for Protection of Human Subjects at the University of Oregon. For a detailed description of the project, please visit its Meta page. This survey is voluntary, and your confidentiality will be protected. You will have the choice of using your Wikipedia User Name during the research or creating a unique pseudonym. You may skip any question you choose, and you may withdraw at any time. By completing the survey, you are providing consent to participate in the research.

If you have any questions about the study, please contact me via my Talk Page (UOJComm) or via email. My faculty advisor is Dr. Ryan Light. If you have any questions regarding your rights as a research participant, please contact the Office for Protection of Human Subjects at the University of Oregon.

Thank you very much.

Sincerely,

Randall Livingstone School of Journalism & Communication University of Oregon UOJComm (talk) 03:57, 22 June 2011 (UTC)

Sydney edit-a-thon invitation
Hi there! You are cordially invited to a classical music edit-a-thon Saturday week (13 October) in Sydney. The theme will be Music of France, to coincide with the ABC Classic FM countdown between 8-14 October. If you are unable to attend in person, we will also be collaborating online during the countdown. Details an attendee list are at Meetup/Sydney/October 2012. Hope you can make it! John Vandenberg 09:17, 3 October 2012 (UTC)

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Sydney edit-a-thon invitation
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Sydney meetup invitation: January 2013
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Hi there! You are cordially invited to an edit-a-thon this Saturday (21 September) in Sydney at the State Library of New South Wales (SLNSW), where you can collaborate with other Wikipedians throughout the day. Andy Carr, a senior librarian at SLNSW will also be helping out. The theme of the edit-a-thon is paralympics sports, but you are free to come along to meet other wiki contributors, and edit other topics.

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Invitation
There is a backstage pass coming up to be followed by an editathon in the State Library of New South Wales on 23 November. This is the first time that an Australian cultural institution has opened its doors to us in this way and will be a special opportunity because the Library is providing: one of its best rooms; its expert curators (along with their expertise and their white gloves); a newly launched website (containing new resources); and of course, items from its collection (including rare and usually unavailable material) which we can look at, learn from, and use, to improve WP articles. For example, on the chosen topic (Australia and WWI), the Library holds many diaries and manuscripts from the period.

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Women in Red World Contest
Hi. We're into the last five days of the Women in Red World Contest. There's a new bonus prize of $200 worth of books of your choice to win for creating the most new women biographies between 0:00 on the 26th and 23:59 on 30th November. If you've been contributing to the contest, thank you for your support, we've produced over 2000 articles. If you haven't contributed yet, we would appreciate you taking the time to add entries to our articles achievements list by the end of the month. Thank you, and if participating, good luck with the finale!

title: User talk:Fipe


text: User talk:66.223.171.5

title: User talk:66.223.171.5


text: User talk:203.144.143.7

title: User talk:203.144.143.7


text:
Totally bounded space

In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered by finitely many subsets of every fixed “size” (where the meaning of “size” depends on the structure of the ambient space).

The term precompact (or pre-compact) is sometimes used with the same meaning, but precompact is also used to mean relatively compact. These definitions coincide for subsets of a complete metric space, but not in general.

In metric spaces

A metric space $$ (M,d) $$ is totally bounded if and only if for every real number $$\varepsilon > 0$$, there exists a finite collection of open balls of radius $$\varepsilon$$ whose centers lie in M and whose union contains $M$. Equivalently, the metric space M is totally bounded if and only if for every $$ \varepsilon >0$$, there exists a finite cover such that the radius of each element of the cover is at most $$\varepsilon$$. This is equivalent to the existence of a finite ε-net. A metric space is said to be totally bounded if every sequence admits a Cauchy subsequence; in complete metric spaces, a set is compact if and only if it is closed and totally bounded.

Each totally bounded space is bounded (as the union of finitely many bounded sets is bounded). The reverse is true for subsets of Euclidean space (with the subspace topology), but not in general. For example, an infinite set equipped with the discrete metric is bounded but not totally bounded: every discrete ball of radius $$\varepsilon = 1/2$$ or less is a singleton, and no finite union of singletons can cover an infinite set.

Uniform (topological) spaces
A metric appears in the definition of total boundedness only to ensure that each element of the finite cover is of comparable size, and can be weakened to that of a uniform structure. A subset $S$ of a uniform space $X$ is totally bounded if and only if, for any entourage $E$, there exists a finite cover of $S$ by subsets of $X$ each of whose Cartesian squares is a subset of $E$. (In other words, $E$ replaces the "size" $ε$, and a subset is of size $E$ if its Cartesian square is a subset of $E$.)

The definition can be extended still further, to any category of spaces with a notion of compactness and Cauchy completion: a space is totally bounded if and only if its (Cauchy) completion is compact.

Examples and elementary properties

 * Every compact set is totally bounded, whenever the concept is defined.
 * Every totally bounded set is bounded.
 * A subset of the real line, or more generally of finite-dimensional Euclidean space, is totally bounded if and only if it is bounded.
 * The unit ball in a Hilbert space, or more generally in a Banach space, is totally bounded (in the norm topology) if and only if the space has finite dimension.
 * Equicontinuous bounded functions on a compact set are precompact in the uniform topology; this is the Arzelà–Ascoli theorem.
 * A metric space is separable if and only if it is homeomorphic to a totally bounded metric space.
 * The closure of a totally bounded subset is again totally bounded.

Comparison with compact sets
In metric spaces, a set is compact if and only if it is complete and totally bounded; without the axiom of choice only the forward direction holds. Precompact sets share a number of properties with compact sets.

 * Like compact sets, a finite union of totally bounded sets is totally bounded.
 * Unlike compact sets, every subset of a totally bounded set is again totally bounded.
 * The continuous image of a compact set is compact. The uniformly continuous image of a precompact set is precompact.

In topological groups
Although the notion of total boundedness is closely tied to metric spaces, the greater algebraic structure of topological groups allows one to trade away some separation properties. For example, in metric spaces, a set is compact if and only if complete and totally bounded. Under the definition below, the same holds for any topological vector space (not necessarily Hausdorff nor complete).

The general logical form of the definition is: a subset $$S$$ of a space $$X$$ is totally bounded if and only if, given any size $$E,$$ there exists a finite cover $$\mathcal{O}$$ of $$S$$ such that each element of $$\mathcal{O}$$ has size at most $$E.$$ $$X$$ is then totally bounded if and only if it is totally bounded when considered as a subset of itself.

We adopt the convention that, for any neighborhood $$U \subseteq X$$ of the identity, a subset $$S \subseteq X$$ is called (') ' if and only if $$(- S) + S \subseteq U.$$ A subset $$S$$ of a topological group $$X$$ is (') ' if it satisfies any of the following equivalent conditions:

 : For any neighborhood $$U$$ of the identity $$0,$$ there exist finitely many $$x_1, \ldots, x_n \in X$$ such that $S \subseteq \bigcup_{j=1}^n \left(x_j + U\right) := \left(x_1 + U\right) + \cdots + \left(x_n + U\right).$  For any neighborhood $$U$$ of $$0,$$ there exists a finite subset $$F \subseteq X$$ such that $$S \subseteq F + U$$ (where the right hand side is the Minkowski sum $$F + U := \{ f + u : f \in F, u \in U \}$$). For any neighborhood $$U$$ of $$0,$$ there exist finitely many subsets $$B_1, \ldots, B_n$$ of $$X$$ such that $$S \subseteq B_1 \cup \cdots \cup B_n$$ and each $$B_j$$ is $$U$$-small. For any given filter subbase $$\mathcal{B}$$ of the identity element's neighborhood filter $$\mathcal{N}$$ (which consists of all neighborhoods of $$0$$ in $$X$$) and for every $$B \in \mathcal{B},$$ there exists a cover of $$S$$ by finitely many $$B$$-small subsets of $$X.$$ $$S$$ is : for every neighborhood $$U$$ of the identity and every countably infinite subset $$I$$ of $$S,$$ there exist distinct $$x, y \in I$$ such that $$x - y \in U.$$ (If $$S$$ is finite then this condition is satisfied vacuously). Any of the following three sets satisfies (any of the above definitions of) being (left) totally bounded: The closure $$\overline{S} = \operatorname{cl}_X S$$ of $$S$$ in $$X.$$ The image of $$S$$ under the canonical quotient $$X \to X / \overline{\{ 0 \}},$$ which is defined by $$x \mapsto x + \overline{\{ 0 \}}$$ (where $$0$$ is the identity element). The sum $$S + \operatorname{cl}_X \{ 0 \}.$$

 * This set being in the list means that the following characterization holds: $$S$$ is (left) totally bounded if and only if $$\operatorname{cl}_X S$$ is (left) totally bounded (according to any of the defining conditions mentioned above). The same characterization holds for the other sets listed below.

The term  usually appears in the context of Hausdorff topological vector spaces. In that case, the following conditions are also all equivalent to $$S$$ being (left) totally bounded:

In the completion $$\widehat{X}$$ of $$X,$$ the closure $$\operatorname{cl}_{\widehat{X}} S$$ of $$S$$ is compact.

Every ultrafilter on $$S$$ is a Cauchy filter.

The definition of  is analogous: simply swap the order of the products.

Condition 4 implies any subset of $$\operatorname{cl}_X \{ 0 \}$$ is totally bounded (in fact, compact; see above). If $$X$$ is not Hausdorff then, for example, $$\{ 0 \}$$ is a compact complete set that is not closed.

Topological vector spaces
Any topological vector space is an abelian topological group under addition, so the above conditions apply. Historically, statement 6(a) was the first reformulation of total boundedness for topological vector spaces; it dates to a 1935 paper of John von Neumann.

This definition has the appealing property that, in a locally convex space endowed with the weak topology, the precompact sets are exactly the bounded sets.

For separable Banach spaces, there is a nice characterization of the precompact sets (in the norm topology) in terms of weakly convergent sequences of functionals: if $$X$$ is a separable Banach space, then $$S \subseteq X$$ is precompact if and only if every weakly convergent sequence of functionals converges uniformly on $$S.$$

Interaction with convexity

The balanced hull of a totally bounded subset of a topological vector space is again totally bounded.

The Minkowski sum of two compact (totally bounded) sets is compact (resp. totally bounded).

In a locally convex (Hausdorff) space, the convex hull and the disked hull of a totally bounded set $$K$$ is totally bounded if and only if $$K$$ is complete.

title: Totally bounded space


text:
Aliquot

Aliquot (a few, some, not many) may refer to:

Mathematics

 * Aliquot part, a proper divisor of an integer
 * Aliquot sum, the sum of the aliquot parts of an integer
 * Aliquot sequence, a sequence of integers in which each number is the aliquot sum of the previous number

Music

 * Aliquot stringing, in stringed instruments, the use of strings which are not struck to make a note, but which resonate sympathetically with struck notes
 * Aliquot stop, an organ stop that adds harmonics or overtones instead of the primary pitch

Sciences

 * Aliquot of a sample, in chemistry and other sciences, a precise portion of a sample or total amount of a liquid (e.g. precisely 25 mL of water taken from 250 mL)
 * Aliquot in pharmaceutics, a method of measuring ingredients below the sensitivity of a scale by proportional dilution with inactive known ingredients
 * Genome aliquoting, the problem of reconstructing an ancestral genome from the genomes of polyploid descendants

Other uses

 * Aliquot part, in the US Public Land Survey System, a subdivision of a section based upon an even division by distances along the edges and not by equal area

title: Aliquot