The Mathematical Legacy of Eduard Čech

1. Front Matter

   Pages 1-8

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2. Life and Work of Eduard Čech

   1. Life and Work of Eduard Čech

      • M. Katětov, J. Novák, A. Švec

      Pages 9-20

3. Bibliography of Eduard Čech

   1. Bibliography of Eduard Čech

      • Miroslav Katětov, Petr Simon

      Pages 21-25

4. Čech-Stone Compactification

   1. Front Matter

      Pages 26-34

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   2. On Bicompact Spaces

      • Eduard Čech

      Pages 38-59

   3. Remark on Bicompact Spaces

      • Bedřich Pospíšil

      Pages 60-61

   4. On Rings of Continuous Functions on Topological Spaces

      • I. Gelfand, A. Kolmogoroff

      Pages 62-66

   5. Stone-Čech Compactifications of Products

      • Irving Glicksberg

      Pages 67-80

   6. Homogeneity Problems in the Theory of Čech Compactifications

      • Walter Rudin

      Pages 81-92

   7. On A Universal Bicompactum of Weight N

      • I. I. Parovičenko

      Pages 93-96

   8. Non-Homogeneity of βP - P

      • Zdeněk Frolík

      Pages 97-99

   9. Weak P-Points in N*

      • K. Kunen

      Pages 100-108

5. Dimension Theory

   1. Front Matter

      Pages 109-125

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   2. On the Dimension of Perfectly Normal Spaces

      • Eduard Čech

      Pages 130-148

   3. Contribution to Dimension Theory

      • Eduard Čech

      Pages 149-160

   4. On The Dimension of Bicompacta

      • O. V. Lokucievskij

      Pages 161-164

   5. Inductive Dimension of Completely Normal Spaces

      • C. H. Dowker

      Pages 165-177

   6. Dimension of metric spaces

      • C. H. Dowker, W. Hurewicz

      Pages 178-183

   7. On The Dimension of Compact Spaces

      • Petr Vopěnka

      Pages 184-190

   8. Bicompacta with Distinct Dimensions Ind and Dim

      • V. V. Filbppov

      Pages 191-195

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.

• Compact space
• Compactification
• evolution
• mathematics
• topology

• Matematický ústav, Praha 8, Czech Republic

  Miroslav Katětov, Petr Simon

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