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Eduard Čech
Eduard Čech (; 29 June 1893 – 15 March 1960) was a Czech mathematician. His research interests included projective differential geometry and topology. He is especially known for the technique known as Stone–Čech compactification (in topology) and the notion of Čech cohomology. He was the first to publish a proof of Tychonoff's theorem in 1937. Biography He was born in Stračov, then in Bohemia, Austria-Hungary, now in the Czech Republic. His father was Čeněk Čech, a policeman, and his mother was Anna Kleplová. After attending the gymnasium in Hradec Králové, Čech was admitted to the Philosophy Faculty of Charles University of Prague in 1912. In 1915 he was drafted into the Austro-Hungarian Army and participated in World War I, after which he completed his undergraduate degree in 1918. He received his doctoral degree in 1920 at Charles University; his thesis, titled ''On Curves and Plane Elements of the Third Order'', was written under the direction of Karel Petr. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stračov
Stračov is a municipality and village in Hradec Králové District in the Hradec Králové Region of the Czech Republic. It has about 300 inhabitants. Administrative parts The village of Klenice is an administrative part of Stračov. Notable people *Eduard Čech Eduard Čech (; 29 June 1893 – 15 March 1960) was a Czech mathematician. His research interests included projective differential geometry and topology. He is especially known for the technique known as Stone–Čech compactification (in topolo ... (1893–1960), mathematician References External links * Villages in Hradec Králové District {{HradecKrálové-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nerve Of A Covering
In topology, the nerve complex of a set family is an abstract complex that records the pattern of intersections between the sets in the family. It was introduced by Pavel Alexandrov and now has many variants and generalisations, among them the Čech nerve of a cover, which in turn is generalised by hypercoverings. It captures many of the interesting topological properties in an algorithmic or combinatorial way. Basic definition Let I be a set of indices and C be a family of sets (U_i)_. The nerve of C is a set of finite subsets of the index set ''I''. It contains all finite subsets J\subseteq I such that the intersection of the U_i whose subindices are in J is non-empty:'', Section 4.3'' :N(C) := \bigg\. In Alexandrov's original definition, the sets (U_i)_ are open subsets of some topological space X. The set N(C) may contain singletons (elements i \in I such that U_i is non-empty), pairs (pairs of elements i,j \in I such that U_i \cap U_j \neq \emptyset), triplets, and so on. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First International Topological Conference
The First International Topological Conference was held in Moscow, 4–10 September, 1935. With presentations by topologists from 10 different countries it constituted the first genuinely international meeting devoted to topology in the world history of the mathematical community. Although a previous mathematical conference had been held in Kharkiv, and attended by Jacques Hadamard, this turned out to be the only truly international conference organised under the Stalin regime. Pavel Aleksandrov played a key role in organising the conference. The foreign delegates were accommodated in major hotels across Moscow, although according to André Weil, the principal form of sustenance was Caviar Canapes served in the conference hall, as no food was available in the hotel restaurants. Presentations Documentation of the conference varies, but this summary was drawn from various sources. Homology Theory * Karol Borsuk: ‘‘On spheroidal spaces’’ * Eduard Čech: "Accessibility and Homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brno
Brno ( , ; german: Brünn ) is a city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava and Svratka rivers, Brno has about 380,000 inhabitants, making it the second-largest city in the Czech Republic after the capital, Prague, and one of the 100 largest cities of the EU. The Brno metropolitan area has almost 700,000 inhabitants. Brno is the former capital city of Moravia and the political and cultural hub of the South Moravian Region. It is the centre of the Czech judiciary, with the seats of the Constitutional Court, the Supreme Court, the Supreme Administrative Court, and the Supreme Public Prosecutor's Office, and a number of state authorities, including the Ombudsman, and the Office for the Protection of Competition. Brno is also an important centre of higher education, with 33 faculties belonging to 13 institutes of higher education and about 89,000 students. Brno Exhibition Centre is among the largest exhibition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turin
Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is mainly on the western bank of the Po (river), Po River, below its Susa Valley, and is surrounded by the western Alps, Alpine arch and Superga Hill. The population of the city proper is 847,287 (31 January 2022) while the population of the urban area is estimated by Larger Urban Zones, Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the Organisation for Economic Co-operation and Development, OECD to have a population of 2.2 million. The city used to be a major European political centre. From 1563, it was the capital of the Duchy of Savoy, then of the Kingdom of Sardinia ruled by the House of Savoy, and the first capital of the Kingdom of Italy from 1861 to 1865. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guido Fubini
Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric. Life Born in Venice, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In 1896 he entered the Scuola Normale Superiore di Pisa, where he studied differential geometry under Ulisse Dini and Luigi Bianchi. His 1900 doctoral thesis was about Clifford parallel, Clifford's parallelism in elliptic spaces.G. Fubini (1900) D.H. Delphenich translatoClifford Parallelism in Elliptic Spaces Laurea thesis, Pisa. After earning his doctorate, he took up a series of professorships. In 1901 he began teaching at the University of Catania in Sicily; shortly afterwards he moved to the University of Genoa; and in 1908 he moved to the Politecnico di Torino, Politecnico in Turin and then the University of Turin, where he would stay for a few decades. During this time his research focused prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fighting occurring throughout Europe, the Middle East, Africa, the Pacific, and parts of Asia. An estimated 9 million soldiers were killed in combat, plus another 23 million wounded, while 5 million civilians died as a result of military action, hunger, and disease. Millions more died in genocides within the Ottoman Empire and in the 1918 influenza pandemic, which was exacerbated by the movement of combatants during the war. Prior to 1914, the European great powers were divided between the Triple Entente (comprising France, Russia, and Britain) and the Triple Alliance (containing Germany, Austria-Hungary, and Italy). Tensions in the Balkans came to a head on 28 June 1914, following the assassination of Archduke Franz Ferdin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austro-Hungarian Army
The Austro-Hungarian Army (, literally "Ground Forces of the Austro-Hungarians"; , literally "Imperial and Royal Army") was the ground force of the Austro-Hungarian Dual Monarchy from 1867 to 1918. It was composed of three parts: the joint army (, "Common Army", recruited from all parts of the country), the Imperial Austrian Landwehr (recruited from Cisleithania), and the Royal Hungarian Honvéd (recruited from Transleithania). In the wake of fighting between the Austrian Empire and the Hungarian Kingdom and the two decades of uneasy co-existence following, Hungarian soldiers served either in mixed units or were stationed away from Hungarian areas. With the Austro-Hungarian Compromise of 1867 the new tripartite army was brought into being. It existed until the disestablishment of the Austro-Hungarian Empire following World War I in 1918. The joint "Imperial and Royal Army" ( or ''k.u.k.'') units were generally poorly trained and had very limited access to new equipment bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hradec Králové
Hradec Králové (; german: Königgrätz) is a city of the Czech Republic. It has about 91,000 inhabitants. It is the capital of the Hradec Králové Region. The historic centre of Hradec Králové is well preserved and is protected by law as an Cultural monument (Czech Republic)#Monument reservations, urban monument reservation, the wider centre is protected as an Cultural monument (Czech Republic)#Monument zones, urban monument zone. Administrative parts Hradec Králové is made up of 21 city parts: *Březhrad *Hradec Králové *Nový Hradec Králové *Kukleny *Malšova Lhota *Malšovice *Moravské Předměstí *Piletice *Plácky *Plačice *Plotiště nad Labem *Pouchov *Pražské Předměstí *Roudnička *Rusek *Slatina *Slezské Předměstí *Svinary *Svobodné Dvory *Třebeš *Věkoše Etymology The city was originally named Hradec, which is a diminutive of ''hrad'' (i.e. "castle"). Later, when it was owned by Bohemian queens, the Králové attribute (from ''král, král ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czech Republic
The Czech Republic, or simply Czechia, is a landlocked country in Central Europe. Historically known as Bohemia, it is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the southeast. The Czech Republic has a hilly landscape that covers an area of with a mostly temperate continental and oceanic climate. The capital and largest city is Prague; other major cities and urban areas include Brno, Ostrava, Plzeň and Liberec. The Duchy of Bohemia was founded in the late 9th century under Great Moravia. It was formally recognized as an Imperial State of the Holy Roman Empire in 1002 and became a kingdom in 1198. Following the Battle of Mohács in 1526, the whole Crown of Bohemia was gradually integrated into the Habsburg monarchy. The Protestant Bohemian Revolt led to the Thirty Years' War. After the Battle of White Mountain, the Habsburgs consolidated their rule. With the dissolution of the Holy Empire in 1806, the Cro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tychonoff's Theorem
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is transcribed ''Tychonoff''), who proved it first in 1930 for powers of the closed unit interval and in 1935 stated the full theorem along with the remark that its proof was the same as for the special case. The earliest known published proof is contained in a 1935 article of Tychonoff, A., "Uber einen Funktionenraum", Mathematical Annals, 111, pp. 762–766 (1935). (This reference is mentioned in "Topology" by Hocking and Young, Dover Publications, Ind.) Tychonoff's theorem is often considered as perhaps the single most important result in general topology (along with Urysohn's lemma). The theorem is also valid for topological spaces based on fuzzy sets.Joseph Goguen, "The Fuzzy Tychonoff Theorem", Journal of Mathematical Analysis and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
