SpringerBriefs in Mathematics

Function Spaces with Uniform, Fine and Graph Topologies

Authors: McCoy, Robert A., Kundu, Subiman, Jindal, Varun

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  • The first research monograph to study exclusively uniform, fine and graph topologies on spaces of continuous functions
  • Studies uniform and fine topologies on spaces of self-homeomorphisms on metric spaces
  • Provides generalizations of known results in the theory of spaces of continuous functions
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-77054-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-77053-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature.

The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.


Reviews

“The monograph provides a detailed introduction to the theory of function spaces with uniform, fine and graph topologies together with complete proofs of the most up to date results in the area. The book will certainly be useful for specialists working in topology and functional analysis as well as for students who need to learn the basics of the theory of the respective function spaces.” (Vladimir Tkachuk, zbMATH 1395.54001, 2018)

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Preliminaries

    McCoy, Robert A. (et al.)

    Pages 1-14

  • Metrizability and Completeness Properties of $$C_{\tau } (X, Y)$$ for $$\tau = d,f, g$$

    McCoy, Robert A. (et al.)

    Pages 15-35

  • Cardinal Functions and Countability Properties

    McCoy, Robert A. (et al.)

    Pages 37-48

  • Connectedness and Path Connectedness of $$C_{\tau }(X, Y)$$ for a Normed Linear Space Y, Where $$\tau = d, f, g$$

    McCoy, Robert A. (et al.)

    Pages 49-62

  • Compactness in $$C_{\tau }(X, Y)$$ for $$\tau = d,f, g$$ and Stone-Weierstrass Approximation Theorem

    McCoy, Robert A. (et al.)

    Pages 63-73

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-77054-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-77053-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Function Spaces with Uniform, Fine and Graph Topologies
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-77054-3
DOI
10.1007/978-3-319-77054-3
Softcover ISBN
978-3-319-77053-6
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XVIII, 106
Topics