Skip to main content
SpringerLink
Log in
Book cover

Rings of Continuous Functions

  • Textbook
  • © 1960

Overview

Authors:
  1. Leonard Gillman

    1. Department of Mathematics, University of Rochester, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Meyer Jerison

    1. Purdue University, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: The university series in higher mathematics (USHM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages i-9
    Download chapter PDF

  2. Functions on a Topological Space

    • Leonard Gillman, Meyer Jerison
    Pages 10-23

  3. Ideals and z-Filters

    • Leonard Gillman, Meyer Jerison
    Pages 24-35

  4. Completely Regular Spaces

    • Leonard Gillman, Meyer Jerison
    Pages 36-53

  5. Fixed Ideals. Compact Spaces

    • Leonard Gillman, Meyer Jerison
    Pages 54-65

  6. Ordered Residue Class Rings

    • Leonard Gillman, Meyer Jerison
    Pages 66-81

  7. The Stone-ÄŒech Compactification

    • Leonard Gillman, Meyer Jerison
    Pages 82-100

  8. Characterization of Maximal Ideals

    • Leonard Gillman, Meyer Jerison
    Pages 101-113

  9. Realcompact Spaces

    • Leonard Gillman, Meyer Jerison
    Pages 114-129

  10. Cardinals of Closed Sets in βX

    • Leonard Gillman, Meyer Jerison
    Pages 130-139

  11. Homomorphisms and Continuous Mappings

    • Leonard Gillman, Meyer Jerison
    Pages 140-153

  12. Embedding in Products of Real Lines

    • Leonard Gillman, Meyer Jerison
    Pages 154-160

  13. Discrete Spaces. Nonmeasurable Cardinals

    • Leonard Gillman, Meyer Jerison
    Pages 161-170

  14. Hyper-Real Residue Class Fields

    • Leonard Gillman, Meyer Jerison
    Pages 171-193

  15. Prime Ideals

    • Leonard Gillman, Meyer Jerison
    Pages 194-215

  16. Uniform Spaces

    • Leonard Gillman, Meyer Jerison
    Pages 216-239

  17. Dimension

    • Leonard Gillman, Meyer Jerison
    Pages 240-265

  18. Back Matter

    Pages 266-300
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Rochester, UK

    Leonard Gillman

  • Purdue University, UK

    Meyer Jerison

Bibliographic Information

  • Book Title: Rings of Continuous Functions

  • Authors: Leonard Gillman, Meyer Jerison

  • Series Title: The university series in higher mathematics

  • DOI: https://doi.org/10.1007/978-1-4615-7819-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1960

  • eBook ISBN: 978-1-4615-7819-2Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: IX, 300

  • Additional Information: Originally published by Van Nostrand

  • Topics: Medicine/Public Health, general

Publish with us

Policies and ethics

Back to top

Search

Navigation