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


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.


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

Bibliographic information