ČECH, Eduard

Č. studied at a grammar school in Hradec Králové, and between 1912 and 1914 attended lectures in mathematics at Charles University in Prague. In 1920 he wrote his PhD dissertation with the title »On flat and curved system of the third degree«. He started dealing with the projective differential geometry and was especially impressed by G. Fubini's discussions. In 1921/22 he obtained a scholarship to go to Italy and study with Fubini in Turin. The result of this fruitful cooperation was the publication of two books, namely Geometria projettiva differenziale and Introduction a la Geometrie Projective différentielle des surfaces. In 1922, Č. wrote his habilitation thesis on differential geometry, becoming a docent at the Charles University of Prague. The following year he was appointed extraordinary professor at Masaryk University in Brno, where he lectured on mathematical analysis and algebra. After receiving much encouragement from the group of mathematicians publishing in the Polish journal Fundamenta Mathematicae, Č. in 1928 became interested in the topology. His early interests in topology were in homology theory, a topic on which his works between 1931 and 1932 were published. He proved duality theorems for manifolds and thus became one of the leading experts on combinatorial topology. In September 1935 he attended a conference on combinatorial topology in Moscow, where he was invited to lecture at the Institute for Advanced Study in Princeton (the USA). Č. was influenced by the work of P.S. Aleksandrov and P. Urysohn and upon his return to Brno in 1936 set up a topology seminar among young mathematicians, where a number of mathematical problems were discussed. The seminar went on to produce 26 scientific papers and only ended when the Czech universities were closed down after the German occupation of Czechoslovakia in 1939. Using a new type of topological spaces which Tikhonov introduced in 1930 and which J. Kelley named »Stone-Cech compactification of regular topological spaces« in Č.'s interpretation became one of the most important tool of general topology and also of some branches of functional analysis. In the same period Č. decided to try to improve methods of teaching mathematics in elementary and secondary schools. Starting in 1938, he organized seminars in Brno for secondary school mathematics teachers. After the war he used his experiences with school teachers to produce a series of school mathematics textbooks. Č. began lecturing at the Faculty of Natural Science of the Charles University in Prague in 1945. He laid the foundation for the establishment of the Central Mathematical Institute of the Czech Academy of Sciences (1952) and later Mathematical Institute of Charles University in Prague. In the field of topology, in addition to the theory of topological spaces, Č. was also concerned with the theory of the compact spaces. In the field of combinatorial topology Č. was primarily interested in the homology and the general manifolds. Between 1921 and 1930 he and Fubini became founders of projective differential geometry. During this period he dealt primarily with manifolds contacts, examining the correspondence and systematic use of duality in the projective spaces. After 1945 he returned to differential geometry and wrote the theory of systematic correspondence between the projective spaces. In doing so, he addressed the problem of congruence of straight lines, which play the leading role in theory of correspondence. His subsequent work was assessed separately. In the latter Č. devoted his attention to the relations between differentiated classes of points on curves as well as its associated objects.