The Stone-Čech Compactification

  • Russell C. Walker

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 83)

Table of contents

  1. Front Matter
    Pages I-X
  2. Russell C. Walker
    Pages 43-69
  3. Russell C. Walker
    Pages 70-94
  4. Russell C. Walker
    Pages 95-119
  5. Russell C. Walker
    Pages 120-135
  6. Russell C. Walker
    Pages 136-159
  7. Russell C. Walker
    Pages 160-186
  8. Russell C. Walker
    Pages 187-219
  9. Russell C. Walker
    Pages 220-242
  10. Russell C. Walker
    Pages 243-296
  11. Back Matter
    Pages 297-334

About this book

Introduction

Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner. The goal of this volume is to make many of these results easily accessible by collecting them in a single source together with the necessary introductory material. The author's interest in this area had its origin in his fascination with the classic text Rings of Continuous Functions by Leonard Gillman and Meyer Jerison. This excellent synthesis of algebra and topology appeared in 1960 and did much to draw attention to the Stone-Cech compactification {3X as a tool to investigate the relationships between a space X and the rings C(X) and C*(X) of real-valued continuous functions. Although in the approach taken here {3X is viewed as the object of study rather than as a tool, the influence of Rings of Continuous Functions is clearly evident. Three introductory chapters make the book essentially self-contained and the exposition suitable for the student who has completed a first course in topology at the graduate level. The development of the Stone­ Cech compactification and the more specialized topological prerequisites are presented in the first chapter. The necessary material on Boolean algebras, including the Stone Representation Theorem, is developed in Chapter 2. A very basic introduction to category theory is presented in the beginning of Chapter 10 and the remainder of the chapter is an introduction to the methods of categorical topology as it relates to the Stone-Cech compactification.

Keywords

Connected space Excel Stone Stone-Tschechsche Kompaktifizierung category theory development extrema form homogenization mapping maximum minimum object tool types

Editors and affiliations

  • Russell C. Walker
    • 1
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61935-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-61937-3
  • Online ISBN 978-3-642-61935-9
  • Series Print ISSN 0071-1136
  • About this book