Metric Spaces

  • Authors
  • Satish Shirali
  • Harkrishan L. Vasudeva

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-22
  3. Pages 23-63
  4. Pages 103-155
  5. Pages 156-169
  6. Pages 170-200
  7. Pages 201-217
  8. Back Matter
    Pages 219-222

About this book

Introduction

This volume provides a complete introduction to metric space theory for undergraduates. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as the Tietze-Urysohn extension theorem, Picard's theorem on ordinary differential equations, and the set of discontinuities of the pointwise limit of a sequence of continuous functions. Key features include:

a full chapter on product metric spaces, including a proof of Tychonoff’s Theorem

a wealth of examples and counter-examples from real analysis, sequence spaces and spaces of continuous functions

numerous exercises – with solutions to most of them – to test understanding.

The only prerequisite is a familiarity with the basics of real analysis: the authors take care to ensure that no prior knowledge of measure theory, Banach spaces or Hilbert spaces is assumed. The material is developed at a leisurely pace and applications of the theory are discussed throughout, making this book ideal as a classroom text for third- and fourth-year undergraduates or as a self-study resource for graduate students and researchers.

Keywords

Compact space Connected space Continuous functions Hilbert space Metric Spaces Open and closed sets connected and compact spaces real analysis set

Bibliographic information

  • DOI https://doi.org/10.1007/1-84628-244-6
  • Copyright Information Springer-Verlag London Limited 2006
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-85233-922-7
  • Online ISBN 978-1-84628-244-7
  • About this book