1935. He said that after reading the book he wrote to Lefschetz that the book
was great, that all the theorems were correct but that none of the proofs were
quite right. He also sent his proofs to Lefschetz. Years later, in 1968, when I
had the opportunity to ask Lefschetz about this, he recalled the incident, saying
that, "Oh yes, I remember that. Cech was quite an extraordinary young man."
Cech's paper which most closely reflects the main topic of the Cech Centennial
Homotopy Conference is the brief communication on higher homotopy groups
presented at the International Congress of Mathematicians held in Ziirich in
1932. In that paper Cech defined the higher homotopy groups. Commenting
on Cech's definition, P. S. Alexandrov wrote in 1961: "This definition did not
meet with the attention it merited; in fact, the commutativity of these groups
for dimensions greater than one was criticized. We must express our admiration
at the intuition and talent of Professor Cech, who defined the homotopy groups
years before W. Hurewitz."
Cech published 30 papers in topology between 1930 and 1938. All those papers
were reprinted in the 1968 text, Topological Papers of Eduard Cech, by Academic
Publishing House of the Czechoslovak Academy of Sciences. The papers contain-
ing some of Cech's major contributions to topology are: On bicompact spaces,
Ann. of Math. 38 (1937), 823-844; Sur la theorie de la dimension, C.R. Acad. Sci.
Paris 193 (1931), 976-977; Sur la dimension des espaces parfaitement normaux,
Bull. Internat. Acad. Tcheque Sci. 33 (1932), 38-55; Contribution to dimension
theory (in Czech), Casopis Pest. Mat. Fys. 62 (1933), 277-291; Theorie generale
de l'homologie dans un espace quelconque, Fund. Math. 19 (1932), 149-183; Les
groupes de Betti d'un complexe infini, Fund. Math. 25 (1935), 33-44; Multi-
plication on a complex, Ann. of Math. 37 (1936), 681-697; Hoherdimensionale
Homotopiegruppen, Verh. des int. Kongr. Ziirich 2 (1932), 203. An extended
biography and a bibliography of Cech's work can be found in the book The
Mathematical Legacy of Eduard Cech, published by Academia, Praha, 1993.
Starting in 1939 all the universities in Bohemia and Moravia were closed for
the duration of the German occupation. After the war, in 1945, Cech returned to
problems in differential geometry. He played a major role in the reconstruction
of mathematical life in Czechoslovakia. He was instrumental in founding the
Mathematical Institute of the Czechoslovak Academy of Sciences in 1950 and
the Mathematical Institute at Charles University in 1956. Cech remained very
active in all aspects of mathematics in Czechoslovakia until his death on March
15, 1960.
Mila Cenkl
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