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The Stone-Čech Compactification

  • Book
  • © 1974

Overview

Editors:
  1. Russell C. Walker

    1. Department of Mathematics, Carnegie-Mellon University, Pittsburgh, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 83)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
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  2. Development of the Stone-Čech Compactification

    • Russell C. Walker
    Pages 1-42

  3. Boolean Algebras

    • Russell C. Walker
    Pages 43-69

  4. On βℕ and ℕ*

    • Russell C. Walker
    Pages 70-94

  5. Non-Homogeneity of Growths

    • Russell C. Walker
    Pages 95-119

  6. Cellularity of Growths

    • Russell C. Walker
    Pages 120-135

  7. Mappings of βX to X*

    • Russell C. Walker
    Pages 136-159

  8. βℕ Revisited

    • Russell C. Walker
    Pages 160-186

  9. Product Theorems

    • Russell C. Walker
    Pages 187-219

  10. Local Connectedness, Continua, and X*

    • Russell C. Walker
    Pages 220-242

  11. βX in Categorical Perspective

    • Russell C. Walker
    Pages 243-296

  12. Back Matter

    Pages 297-334
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Carnegie-Mellon University, Pittsburgh, USA

    Russell C. Walker

Bibliographic Information

  • Book Title: The Stone-Čech Compactification

  • Editors: Russell C. Walker

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-61935-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg New York 1974

  • Hardcover ISBN: 978-3-540-06699-6Published: 10 December 1974

  • Softcover ISBN: 978-3-642-61937-3Published: 12 October 2011

  • eBook ISBN: 978-3-642-61935-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 334

  • Topics: Geology, Functional Analysis

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