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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 Pe ... [...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 division Stračov consists of two municipal parts (in brackets population according to the 2021 census): *Stračov (250) *Klenice (39) Demographics 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 topo ... (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 is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents within the city limits, over 19.1 million residents in the urban area, and over 21.5 million residents in Moscow metropolitan area, its 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 List of largest cities, largest cities, being the List of European cities by population within city limits, most populous city entirely in Europe, the largest List of urban areas in Europe, urban and List of metropolitan areas in Europe, metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow became the capital of the Grand Principality of Moscow, which led the unification of the Russian lan ... [...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 History of the Soviet Union (1927–1953), 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’ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brno
Brno ( , ; ) is a Statutory city (Czech Republic), city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava (river), Svitava and Svratka (river), Svratka rivers, Brno has about 403,000 inhabitants, making it the second-largest city in the Czech Republic after the capital, Prague, and one of the List of cities in the European Union by population within city limits, 100 largest cities of the European Union. The Brno metropolitan area has approximately 730,000 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 Judiciary of the Czech Republic, Czech judiciary, with the seats of the Constitutional Court of the Czech Republic, Constitutional Court, the Supreme Court of the Czech Republic, Supreme Court, the Supreme Administrative Court of the Czech Republic, Supreme Administrative Court, and the Supreme Public Prosecutor's Office, and a number of state ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turin
Turin ( , ; ; , then ) 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), River Po, below its Susa Valley, and is surrounded by the western Alpine arch and Superga hill. The population of the city proper is 856,745 as of 2025, while the population of the urban area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million. The city was historically a major European political centre. From 1563, it was the capital of the Duchy of Savoy, then of the Kingdom of Sardinia (1720–1861), Kingdom of Sardinia ruled by the House of Savoy, and the first capital of the Kingdom of Italy from 1861 to 1865. Turin is sometimes called "the cradle of Italian liberty" for having been the politi ... [...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'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 in Turin and then the University of Turin, where he stayed for a few decades. During this time his research focused primarily on topics in mathematical a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting took place mainly in European theatre of World War I, Europe and the Middle Eastern theatre of World War I, Middle East, as well as in parts of African theatre of World War I, Africa and the Asian and Pacific theatre of World War I, Asia-Pacific, and in Europe was characterised by trench warfare; the widespread use of Artillery of World War I, artillery, machine guns, and Chemical weapons in World War I, chemical weapons (gas); and the introductions of Tanks in World War I, tanks and Aviation in World War I, aircraft. World War I was one of the List of wars by death toll, deadliest conflicts in history, resulting in an estimated World War I casualties, 10 million military dead and more than 20 million wounded, plus some 10 million civilian de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austro-Hungarian Army
The Austro-Hungarian Army, also known as the Imperial and Royal Army,; was the principal ground force of Austria-Hungary from 1867 to 1918. It consisted of three organisations: the Common Army (, recruited from all parts of Austria-Hungary), the Imperial-Royal Landwehr (recruited from Cisleithania) and the Royal Hungarian Honvéd (recruited from Transleithania). In the wake of fighting between the Austrian Empire and the Kingdom of Hungary and the subsequent two decades of uneasy co-existence, Hungarian troops served either in ethnically mixed units or were stationed away from Hungarian regions. With the Austro-Hungarian Compromise of 1867, the Austro-Hungarian Army was brought into being. It existed until the disestablishment of Austria-Hungary in 1918 following the end of World War I. Common Army units were generally poorly trained and had very limited access to new equipment, because the governments of the Austrian and Hungarian parts of the empire often preferred to ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hradec Králové
Hradec Králové (; ) is a city of the Czech Republic. It has about 94,000 inhabitants. It is the capital of the Hradec Králové Region. The historic centre of Hradec Králové is well preserved and is protected 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 division Hradec Králové consists of 21 municipal parts (in brackets population according to the 2021 census): *Březhrad (899) *Hradec Králové (14,782) *Kukleny (2,617) *Malšova Lhota (869) *Malšovice (2,557) *Moravské Předměstí (4,966) *Nový Hradec Králové (22,458) *Piletice (186) *Plácky (1,108) *Plačice (737) *Plotiště nad Labem (2,087) *Pouchov (2,007) *Pražské Předměstí (13,045) *Roudnička (873) *Rusek (411) *Slatina (742) *Slezské Předměstí (8,948) *Svinary (1,064) *Svobodné Dvory (2,632) *Třebeš (7,225) *Věkoše (2,436) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czech Republic
The Czech Republic, also known as Czechia, and historically known as Bohemia, is a landlocked country in Central Europe. The country 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 Humid continental climate, 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 Estate of the Holy Roman Empire in 1002 and became Kingdom of Bohemia, a kingdom in 1198. Following the Battle of Mohács in 1526, all of the Lands of the Bohemian Crown were gradually integrated into the Habsburg monarchy. Nearly a hundred years later, the Protestantism, Protestant Bohemian Revolt led to the Thirty Years' War. After the Battle of White ... [...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 by Tychonoff, . 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. Topological definitions The theorem depends crucially upon the precise definitions of compactness and of the product topology; in fact, Tychonoff's 1935 paper defines the product topology for the first time. Conversely, part of its importance is to gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
