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Topologies and Uniformities

  • Ioan Mackenzie James

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ioan Mackenzie James
    Pages 1-27
  3. Ioan Mackenzie James
    Pages 29-46
  4. Ioan Mackenzie James
    Pages 47-61
  5. Ioan Mackenzie James
    Pages 63-73
  6. Ioan Mackenzie James
    Pages 75-86
  7. Ioan Mackenzie James
    Pages 87-102
  8. Ioan Mackenzie James
    Pages 103-125
  9. Ioan Mackenzie James
    Pages 127-144
  10. Ioan Mackenzie James
    Pages 145-164
  11. Ioan Mackenzie James
    Pages 165-177
  12. Ioan Mackenzie James
    Pages 179-188
  13. Ioan Mackenzie James
    Pages 189-201
  14. Back Matter
    Pages 203-230

About this book

Introduction

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.

Keywords

Compact space DEX Microsoft Access form function functional functions topology

Authors and affiliations

  • Ioan Mackenzie James
    • 1
  1. 1.Mathematical InstituteOxford UniversityOxfordUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3994-2
  • Copyright Information Springer-Verlag London 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-061-3
  • Online ISBN 978-1-4471-3994-2
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site