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Topologies and Uniformities

  • Textbook
  • © 1999

Overview

Authors:
  1. Ioan Mackenzie James

    1. Mathematical Institute, Oxford University, Oxford, UK

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  • Revised edition of an already excellent text
  • Accessible to undergraduates with detailed explanations and exercises
  • Contains a new chapter on historical aspects

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Topological Spaces

    • Ioan Mackenzie James
    Pages 1-27

  3. Continuity

    • Ioan Mackenzie James
    Pages 29-46

  4. The Induced Topology and Its Dual

    • Ioan Mackenzie James
    Pages 47-61

  5. Open Functions and Closed Functions

    • Ioan Mackenzie James
    Pages 63-73

  6. Compact Spaces

    • Ioan Mackenzie James
    Pages 75-86

  7. Separation Conditions

    • Ioan Mackenzie James
    Pages 87-102

  8. Uniform Spaces

    • Ioan Mackenzie James
    Pages 103-125

  9. The Uniform Topology

    • Ioan Mackenzie James
    Pages 127-144

  10. Connectedness

    • Ioan Mackenzie James
    Pages 145-164

  11. Countability and Related Topics

    • Ioan Mackenzie James
    Pages 165-177

  12. Functional Separation Conditions

    • Ioan Mackenzie James
    Pages 179-188

  13. Completeness and Completion

    • Ioan Mackenzie James
    Pages 189-201

  14. Back Matter

    Pages 203-230
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Keywords

About this book

This book is based on lectures I have given to senior undergraduate and graduate audiences at Oxford and elsewhere over the years. My aim has been to provide an outline of both the topological theory and the uniform theory, with an emphasis on the relation between the two. Although I hope that the prospective specialist may find it useful as an introduction it is the non-specialist I have had more in mind in selecting the contents. Thus I have tended to avoid the ingenious examples and counterexamples which often occupy much of the space in books on general topology, and I have tried to keep the number of definitions down to the essential minimum. There are no particular prerequisites but I have worked on the assumption that a potential reader will already have had some experience of working with sets and functions and will also be familiar with the basic concepts of algebra and analysis. An earlier version of the present book appeared in 1987 under the title Topo­ logical and Uniform Spaces. When the time came for a new edition I came to the conclusion that, rather than just making the necessary corrections, it would be better to make more substantial alterations. Parts of the text have been rewritten and new material, including new diagrams, added.

Authors and Affiliations

  • Mathematical Institute, Oxford University, Oxford, UK

    Ioan Mackenzie James

Bibliographic Information

  • Book Title: Topologies and Uniformities

  • Authors: Ioan Mackenzie James

  • Series Title: Springer Undergraduate Mathematics Series

  • DOI: https://doi.org/10.1007/978-1-4471-3994-2

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 1999

  • Softcover ISBN: 978-1-85233-061-3Published: 09 April 1999

  • eBook ISBN: 978-1-4471-3994-2Published: 29 June 2013

  • Series ISSN: 1615-2085

  • Series E-ISSN: 2197-4144

  • Edition Number: 1

  • Number of Pages: XV, 230

  • Number of Illustrations: 22 b/w illustrations

  • Topics: Topology, Algebraic Topology

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