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Foundations of Topology

An Approach to Convenient Topology

  • Gerhard Preuss

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Gerhard Preuss
    Pages 1-27
  3. Gerhard Preuss
    Pages 29-43
  4. Gerhard Preuss
    Pages 45-89
  5. Gerhard Preuss
    Pages 91-110
  6. Gerhard Preuss
    Pages 111-159
  7. Gerhard Preuss
    Pages 161-179
  8. Gerhard Preuss
    Pages 181-217
  9. Back Matter
    Pages 255-303

About this book

Introduction

A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this setting semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, e.g. simple convergence, continuous convergence and uniform convergence. Various interesting results are presented which cannot be obtained by using topological or uniform spaces in the usual context. The text is self-contained with the exception of the last chapter, where the intuitive concept of nearness is incorporated in Convenient Topology (there exist already excellent expositions on nearness spaces).

Keywords

algebra function space topology

Authors and affiliations

  • Gerhard Preuss
    • 1
  1. 1.Institut für Mathematik IFreie Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-0489-3
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-3940-6
  • Online ISBN 978-94-010-0489-3
  • Buy this book on publisher's site