Modern Analysis and Topology

  • Norman R. Howes

Part of the Universitext book series (UTX)

Table of contents

  1. Topology

    1. Front Matter
      Pages xxix-xxix
    2. Front Matter
      Pages i-xxviii
    3. Norman R. Howes
      Pages 1-42
    4. Norman R. Howes
      Pages 43-61
    5. Norman R. Howes
      Pages 62-82
    6. Norman R. Howes
      Pages 110-155
    7. Norman R. Howes
      Pages 156-201
    8. Norman R. Howes
      Pages 202-228
    9. Norman R. Howes
      Pages 229-263
    10. Norman R. Howes
      Pages 264-283
    11. Norman R. Howes
      Pages 284-316
    12. Norman R. Howes
      Pages 317-369
    13. Norman R. Howes
      Pages 370-393
  2. Back Matter
    Pages 394-403

About this book

Introduction

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para­ compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.

Keywords

Banach Space Compact space Compactification Derivative Hilbert space Homeomorphism Maximum Metrization theorem calculus compactness differential equation measure

Authors and affiliations

  • Norman R. Howes
    • 1
  1. 1.Institute for Defense AnalysesAlexandriaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0833-4
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97986-1
  • Online ISBN 978-1-4612-0833-4
  • Series Print ISSN 0172-5939
  • About this book
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