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Modern Analysis and Topology

  • Textbook
  • © 1995
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Overview

Authors:
  1. Norman R. Howes

    1. Institute for Defense Analyses, Alexandria, USA

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Part of the book series: Universitext (UTX)

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Table of contents (12 chapters)

  1. Topology

    1. Front Matter

      Pages xxix-xxix
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    2. Front Matter

      Pages i-xxviii
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    3. Metric Spaces

      • Norman R. Howes
      Pages 1-42
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    4. Uniformities

      • Norman R. Howes
      Pages 43-61
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    5. Transfinite Sequences

      • Norman R. Howes
      Pages 62-82
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    6. Completeness, Cofinal Completeness And Uniform Paracompactness

      • Norman R. Howes
      Pages 83-109
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    7. Fundamental Constructions

      • Norman R. Howes
      Pages 110-155
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    8. Paracompactifications

      • Norman R. Howes
      Pages 156-201
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    9. Realcompactifications

      • Norman R. Howes
      Pages 202-228
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    10. Measure and Integration

      • Norman R. Howes
      Pages 229-263
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    11. Haar Measure in Uniform Spaces

      • Norman R. Howes
      Pages 264-283
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    12. Uniform Measures

      • Norman R. Howes
      Pages 284-316
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    13. Spaces of Functions

      • Norman R. Howes
      Pages 317-369
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    14. Uniform Differentiation

      • Norman R. Howes
      Pages 370-393
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  2. Back Matter

    Pages 394-403
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Keywords

About this book

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.

Authors and Affiliations

  • Institute for Defense Analyses, Alexandria, USA

    Norman R. Howes

Bibliographic Information

  • Book Title: Modern Analysis and Topology

  • Authors: Norman R. Howes

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-0833-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1995

  • Softcover ISBN: 978-0-387-97986-1Published: 23 June 1995

  • eBook ISBN: 978-1-4612-0833-4Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XXVIII, 444

  • Topics: Analysis, Topology

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