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Function Spaces with Uniform, Fine and Graph Topologies

  • Robert A. McCoy
  • Subiman Kundu
  • Varun Jindal

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 1-14
  3. Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 15-35
  4. Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 37-48
  5. Robert A. McCoy, Subiman Kundu, Varun Jindal
    Pages 75-100
  6. Back Matter
    Pages 101-106

About this book

Introduction

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.


Keywords

Function space topologies Spaces of homeomorphisms uniform spaces metrizability first countability cardinal function properties completeness properties compactness connectedness

Authors and affiliations

  • Robert A. McCoy
    • 1
  • Subiman Kundu
    • 2
  • Varun Jindal
    • 3
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia
  3. 3.Department of MathematicsMalaviya National Institute of TechnologyJaipurIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77054-3
  • Copyright Information The Author(s) 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77053-6
  • Online ISBN 978-3-319-77054-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site