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Foundations of Topology

An Approach to Convenient Topology

  • Book
  • © 2002

Overview

Authors:
  1. Gerhard Preuss

    1. Institut für Mathematik I, Freie Universität Berlin, Berlin, Germany

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Preliminaries

    • Gerhard Preuss
    Pages 1-27

  3. Topological Constructs

    • Gerhard Preuss
    Pages 29-43

  4. Reflections and Coreflections

    • Gerhard Preuss
    Pages 45-89

  5. Topological Universes

    • Gerhard Preuss
    Pages 91-110

  6. Completions of Semiuniform Convergence Spaces

    • Gerhard Preuss
    Pages 111-159

  7. Connectedness Properties

    • Gerhard Preuss
    Pages 161-179

  8. Function Spaces

    • Gerhard Preuss
    Pages 181-217

  9. Relations between Semiuniform Convergence Spaces and Merotopic Spaces (including Nearness Spaces)

    • Gerhard Preuss
    Pages 219-253

  10. Back Matter

    Pages 255-303
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Keywords

About this book

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).

Authors and Affiliations

  • Institut für Mathematik I, Freie Universität Berlin, Berlin, Germany

    Gerhard Preuss

Bibliographic Information

  • Book Title: Foundations of Topology

  • Book Subtitle: An Approach to Convenient Topology

  • Authors: Gerhard Preuss

  • DOI: https://doi.org/10.1007/978-94-010-0489-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-0891-7Published: 31 October 2002

  • Softcover ISBN: 978-94-010-3940-6Published: 02 November 2012

  • eBook ISBN: 978-94-010-0489-3Published: 27 June 2011

  • Edition Number: 1

  • Number of Pages: XVIII, 303

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Topology, Algebraic Topology, Category Theory, Homological Algebra, Functional Analysis

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