Rings of Continuous Functions

  • Leonard Gillman
  • Meyer Jerison

Part of the The University Series in Higher Mathematics book series (USHM)

Table of contents

  1. Front Matter
    Pages i-9
  2. Leonard Gillman, Meyer Jerison
    Pages 10-23
  3. Leonard Gillman, Meyer Jerison
    Pages 24-35
  4. Leonard Gillman, Meyer Jerison
    Pages 36-53
  5. Leonard Gillman, Meyer Jerison
    Pages 54-65
  6. Leonard Gillman, Meyer Jerison
    Pages 66-81
  7. Leonard Gillman, Meyer Jerison
    Pages 82-100
  8. Leonard Gillman, Meyer Jerison
    Pages 101-113
  9. Leonard Gillman, Meyer Jerison
    Pages 114-129
  10. Leonard Gillman, Meyer Jerison
    Pages 130-139
  11. Leonard Gillman, Meyer Jerison
    Pages 140-153
  12. Leonard Gillman, Meyer Jerison
    Pages 154-160
  13. Leonard Gillman, Meyer Jerison
    Pages 161-170
  14. Leonard Gillman, Meyer Jerison
    Pages 171-193
  15. Leonard Gillman, Meyer Jerison
    Pages 194-215
  16. Leonard Gillman, Meyer Jerison
    Pages 216-239
  17. Leonard Gillman, Meyer Jerison
    Pages 240-265
  18. Back Matter
    Pages 266-300

About this book

Introduction

This book is addressed to those who know the meaning of each word in the title: none is defined in the text. The reader can estimate the knowledge required by looking at Chapter 0; he should not be dis­ couraged, however, if he finds some of its material unfamiliar or the presentation rather hurried. Our objective is a systematic study of the ring C(X) of all real-valued continuous functions on an arbitrary topological space X. We are con­ cerned with algebraic properties of C(X) and its subring C*(X) of bounded functions and with the interplay between these properties and the topology of the space X on which the functions are defined. Major emphasis is placed on the study of ideals, especially maximal ideals, and on their associated residue class rings. Problems of extending continuous functions from a subspace to the entire space arise as a necessary adjunct to this study and are dealt with in considerable detail. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5 and the beginning of Chapter 10, presents the fundamental aspects of the subject insofar as they can be discussed without introducing the Stone-Cech compactification. In Chapter 3, the study is reduced to the case of completely regular spaces.

Keywords

Compactification algebra class function functions knowledge material maximum object presentation residue science and technology space subject topology

Authors and affiliations

  • Leonard Gillman
    • 1
  • Meyer Jerison
    • 2
  1. 1.Department of MathematicsUniversity of RochesterUK
  2. 2.Purdue UniversityUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7819-2
  • Copyright Information Springer-Verlag New York 1960
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90120-6
  • Online ISBN 978-1-4615-7819-2
  • About this book