EDUARD CECH xi

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

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