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Eduard Čech (; 29 June 1893 – 15 March 1960) was a Czech
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. His research interests included
projective differential geometry In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations o ...
and
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
. He is especially known for the technique known as
Stone–Čech compactification In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space ''X'' to a compact Hausdorff space ''βX''. The Sto ...
(in topology) and the notion of
Čech cohomology In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Motivation Let ''X'' be a topo ...
. He was the first to publish a proof of
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 t ...
in 1937.


Biography

He was born in Stračov, then in Bohemia,
Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...
, now in the
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. Th ...
. His father was Čeněk Čech, a policeman, and his mother was Anna Kleplová. After attending the gymnasium in
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 a ...
, Čech was admitted to the Philosophy Faculty of
Charles University ) , image_name = Carolinum_Logo.svg , image_size = 200px , established = , type = Public, Ancient , budget = 8.9 billion CZK , rector = Milena Králíčková , faculty = 4,057 , administrative_staff = 4,026 , students = 51,438 , underg ...
of Prague in 1912. In 1915 he was drafted into the
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 arm ...
and participated in
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
, 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. In 1921–1922 he collaborated with
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 ...
in
Turin Turin ( , 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. Th ...
, Italy. He taught at
Masaryk University Masaryk University (MU) ( cs, Masarykova univerzita; la, Universitas Masarykiana Brunensis) is the second largest university in the Czech Republic, a member of the Compostela Group and the Utrecht Network. Founded in 1919 in Brno as the sec ...
in Brno and at Charles University.
Ivo Babuška Ivo M. Babuška (born March 22, 1926, in Prague) is a Czech- American mathematician, noted for his studies of the finite element method and the proof of the Babuška–Lax–Milgram theorem in partial differential equations. One of the celebrated ...
, Vlastimil Dlab,
Zdeněk Frolík Zdeněk Frolík (March 10, 1933 – May 3, 1989) was a Czech mathematician. His research interests included topology and functional analysis. In particular, his work concerned covering properties of topological spaces, ultrafilters, homogenei ...
, Věra Trnková, and Petr Vopěnka have been doctoral students of Čech. He attended the First International Topological Conference held in
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 ...
4–10 September 1935. He made two presentations there: "Accessibility and homology" and "
Betti group In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic top ...
s with different coefficient groups". He died in
Prague Prague ( ; cs, Praha ; german: Prag, ; la, Praga) is the capital and largest city in the Czech Republic, and the historical capital of Bohemia. On the Vltava river, Prague is home to about 1.3 million people. The city has a temperate ...
in 1960.


Publications

* * *


See also

*
Čech closure operator In topology, a preclosure operator, or Čech closure operator is a map between subsets of a set, similar to a topological closure operator, except that it is not required to be idempotent. That is, a preclosure operator obeys only three of the fou ...
*
Čech cohomology In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Motivation Let ''X'' be a topo ...
* Čech nerve *
Stone–Čech compactification In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space ''X'' to a compact Hausdorff space ''βX''. The Sto ...
*
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 t ...


References


External links


List of publications from ''Czech Digital Mathematics Library''
1893 births 1960 deaths People from Hradec Králové District People from the Kingdom of Bohemia Czech mathematicians 20th-century Czech mathematicians Topologists Charles University alumni Institute for Advanced Study visiting scholars Masaryk University faculty Charles University faculty Austro-Hungarian military personnel of World War I {{Europe-mathematician-stub