Opletalova 38, 110 00 Staré Město, Czechia
Čech attended lectures on mathematics at the Charles University of Prague from 1912 to 1914. In 1920 he took his degree in mathematics at the University of Prague.
After studying at the Gymnasium in Hradec Kralove, Čech attended lectures on mathematics at the Charles University of Prague from 1912 to 1914. In 1920 he took his degree in mathematics at the University of Prague. Even his first works showed his mathematical talent. He began to study differential projective properties of geometrical figures and became interested in the work of Guido Fubini. He obtained a scholarship for the school year 1921-1922 that enabled him to study with Fubini in Turin.
In 1922 Čech was appointed associate professor of mathematics at the University of Prague; on this occasion he presented a study on differential geometry. From 1923 he was professor of mathematics at the Faculty of Natural Sciences of the University of Brno, lecturing on mathematical analysis and algebra. From 1928 on, Čech was interested in topology, inspired by the works of mathematicians who contributed to the Polish journal Fundamenta mathematicae. His work from 1932 on, devoted to the general theory of homology in arbitrary spaces, the general theory of varieties, and theorems of duality, showed him to be one of the foremost experts in combinatorial topology. In September 1935 he was invited to lecture at the Institute for Advanced Study at Princeton.
Čech returned to Brno in 1936 and founded a topology seminar among the young mathematicians there. During the three years the seminar was in existence, the works of P. S. Alexandrov and Pavel Uryson were studied and twenty-six papers were written. The group disbanded at the closing of Czech universities following the German occupation in 1939. In his paper “On Bicompact Spaces” Čech stated precisely the possibilities of utilizing a new type of topological space, which later came to be known as Čech’s bicompact envelope or as Stone and Čech’s compact envelope. His interpretation became a very important tool of general topology and also of some branches of functional analysis. He was also concerned with the improvement of the teaching of mathematics in secondary schools. He organized courses for secondary school teachers in Brno in 1938-1939; the results are shown in a series of mathematics textbooks for secondary schools that were written under his guidance after World War II.
In 1945 Čech went to the faculty of Natural Sciences of Charles University in Prague. There he was instrumental in founding two research centers: the Mathematical Institute of the Czechoslovak Academy of Science (1952) and the Mathematical Institute of Charles University. In topology, in addition to the theory of topological spaces, Čech worked on the theories of dimension and continuous spaces. In combinatory topology he was concerned primarily with the theory of homology and general varieties. He was most active in differential geometry from 1921 to 1930, when he became one of the founders of systematic projective differential geometry; he dedicated himself chiefly to problems of the connection of varieties, to the study of correspondences, and to systematic utilization of duality in projective spaces. After 1945 he returned to problems of differential geometry and developed a systematic theory of correspondences between projective spaces. His attention was then drawn to the problems of congruences of straight lines that play a significant role in the theory of correspondences. Somewhat different is his work on the relations between the differential classes of points of a curve and the object attached to it. A number of his ideas were elaborated in the works of his students. They can also be found in some of his manuscripts that have been preserved, published in part in 1968.