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Function Spaces with Uniform, Fine and Graph Topologies

  • Book
  • © 2018

Overview

Authors:
  1. Robert A. McCoy

    1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

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  2. Subiman Kundu

    1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

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    You can also search for this author in PubMed   Google Scholar

  3. Varun Jindal

    1. Department of Mathematics, Malaviya National Institute of Technology, Jaipur, India

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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

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Preliminaries

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 1-14

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

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 15-35

  4. Cardinal Functions and Countability Properties

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 37-48

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

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 49-62

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

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 63-73

  7. Spaces of Homeomorphisms

    • Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 75-100

  8. Back Matter

    Pages 101-106
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Keywords

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)

Authors and Affiliations

  • Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

    Robert A. McCoy

  • Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

    Subiman Kundu

  • Department of Mathematics, Malaviya National Institute of Technology, Jaipur, India

    Varun Jindal

Bibliographic Information

  • Book Title: Function Spaces with Uniform, Fine and Graph Topologies

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

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-77054-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s) 2018

  • Softcover ISBN: 978-3-319-77053-6Published: 25 April 2018

  • eBook ISBN: 978-3-319-77054-3Published: 21 April 2018

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XVIII, 106

  • Topics: Topology

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