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Eduard Cech's studied at the Charles University of Prague but these studies were interrupted by World War I and, although he went there in 1912, he could not graduate before 1920. His interest in a new area of mathematics, namely projective differential geometry, led to his obtaining a scholarship to study with Fubini in Turin. He studied there between 1921 and 1922 and Cech was later to write two books with Fubini which were published in 1927 and 1931.
After leaving Italy, Cech wrote his habilitation thesis, becoming a lecturer at Masarky University in Brno. There he lectured on analysis and algebra, becoming a professor in 1928.
Cech became interested in topology, in particular he became one of the foremost experts on combinatorial topology. His early interests in topology were in homology theory, a topic on which he published in 1932, and he proved duality theorems for manifolds. His aim was to bring together point-set topology and algebraic topology with his 1932 paper. In this paper, which introduces the topic which today is called the Cech homology theory, Cech also introduced the notion of the inverse limit.
At the International Congress of Mathematicians in Zurich in 1932, Cech introduced the notion of higher homotopy groups of a space. Two years later Cech extended his work on homology to local homology. On hearing Cech talk about his results at a conference in Moscow, Lefschetz invited him to visit Princeton and Cech made the visit in 1935.
Cech was then influenced by the work of Aleksandrov and Urysohn and he set up a topology seminar at Brno in 1936 which went on to produce 26 papers in 3 years. One of these papers was Cech's paper On bicompact spaces which introduces what today is called the Stone-Cech compactification of regular topological spaces.
Cech's Brno seminar only ended when the Czech universities were closed down at the onset of World War II. Cech, however, tried to continue the work of his seminar despite the War and it continued to meet at the house of one of his students until 1941. At this point the student was arrested by the Gastapo and the seminar could no longer continue.
After the World War II Cech went to the Charles University of Prague and began an administrative career. He became Director of the Mathematical Research Institute of the Czech Academy in 1947, Director of the Central Mathematical Institute in 1950, and Director of the Czechoslovak Academy in 1952. However in that year he returned to the Charles University of Prague to head the new Mathematical Institute there. In the 1950's his mathematical interests turned to differential geometry; he wrote17 papers on that topic.
Cech's work in topology is fundamental but his work was also important in the development of functional analysis.
References (14 books/articles)