The Mathematical Legacy of Eduard Čech

ISBN-13: 9783034875264 / Angielski / Miękka / 2012 / 445 str.

Katetov;Simon

Opis

The work of Professor Eduard Cech had a si~ificant influence on the development of algebraic and general topology and differential geometry. This book, which appears on the occasion of the centenary of Cech's birth, contains some of his most important papers and traces the subsequent trends emerging from his ideas. The body of the book consists of four chapters devoted to algebraic topology, Cech-Stone compactification, dimension theory and differential geometry. Each of these includes a selection of Cech's papers, a brief summary of some results which followed from his work or constituted solutions to the problems he posed, and several selected papers by various authors concerning the areas of study he initiated. The book also contains a concise biography borrowed with minor changes from the book Topological papers of E. tech, a list of Cech's publications and a very brief note on his activity in the didactics of mathematics. The editors wish to express their sincere gratitude to all who contributed to the completion and publication of this book.

Spis treści

Life and work of Eduard ?ech.- Bibliography of E. ?ech.- ?ech-Stone Compactification.- On Bicompact Spaces, Annals of Mathematics 38, 1937.- Remark on Bicompact Spaces, Annals of Mathematics 38, 1937.- On Rings of Continuous Functions on Topological Spaces, Comptes Rendus (Doklady) de l’Académie des Sciences de l’URSS 22, 1939.- Stone-?ech Compactifications of Products, Transactions of Amer. Math. Soc. 90, 1959.- Stone-?ech Homogeneity Problems in the Theory of ?ech Compactifications, Duke Math. J. 23, 1956.- On a Universal Bicompactum of Weight N, Doklady Akad. Nauk. SSSR 150, 1963. (Translated from Russian by P. Simon).- Non-Homogeneity of ?P - P, Comment. Math. Univ. Carolinae 8, 1967.- Weak P-Points in N*, Colloquia Math. Soc. J. Bolyai 23, 1978.- Dimension Theory.- On the Dimension of Perfectly Normal Spaces, Bull. Intern. Acad. Tcheque Sci. 33, 1932. (Translated from French by J. Vanzura).- Contribution to Dimension Theory, ?asopis P?st. Mat. Fys. 62, 1933. (Translated from Czech by P. Simon).- On the Dimension of Bicompacta, Doklady Akad. Nauk SSSR 67, 1949. (Translated from Russian by P. Simon).- Inductive Dimension of Completely Normal Spaces, Quart. J. Math. Oxford Ser. (2) 4, 1953.- Dimension of Metric Spaces, Fundamenta Mathematicae 43, 1956.- On the Dimension of Compact Spaces, Czechoslovak Math. J. 8, 1958. (Translated from Russian by P. Simon).- Bicompacta with Distinct Dimensions ind and dim, Doklady Akad. Nauk. SSSR 192, 1970. (Translated from Russian by P. Simon).- A Hereditarily Normal Strongly Zero-Dimensional Space with a Subspace of Positive Dimension and an N-Compact Space of Positive Dimension, Fundamenta Mathematicae 97, 1977.- Spaces with Noncoinciding Dimensions, Proceedings of Amer. Math. Soc. 94, 1985.- Algebraic Topology.- General Homology Theory in an Arbitrary Space, Fundamenta Mathematicae 10, 1932. (Translated from French by J. Vanžura).- Betti Groups of an Infinite Complex, Fundamenta Mathematicae 25, 1935. (Translated from French by J. Vanžura).- Multiplications On a Complex, Annals of Math. 37, 1936.- On Generalized Manifolds, American J. of Math. 55, 1933.- ?ech Cohomology Theory and the Axioms, Annals of Math. 51, 1950.- Differential Geometry.- On the Surfaces All Segre Curves of Which Are Plane Curves, Publ. Fac. Sci. Univ. Masaryk 11, 1922. (Translated from French by J. Vanžura).- Developable Transformations of Line Congruences, Czechoslovak Math. J. 6, 1956. (Translated from French by J. Vanžura).- On the Differential Geometry of a Surface Embedded in a Three Dimensional Space With Projective Connection, Czechoslovak Math. J. 11, 1961. (Translated from French by J. Vanžura).- Order of Holonomy of a Surface With Projective Connection, ?asopis P?st. Mat. 96, 1971.- Geometric Deformations of the Evolution Equations and Bäcklund Transformations, Physica 18D, 1986.- Professor ?ech and Didactics of Mathematics.- Acknowledgement.