Introduction to Metric and Topological Spaces

Introduction to Metric and Topological Spaces

Paperback Oxford Mathematics

By (author) Wilson A. Sutherland

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  • Publisher: Oxford University Press
  • Format: Paperback | 224 pages
  • Dimensions: 152mm x 230mm x 14mm | 340g
  • Publication date: 4 October 2009
  • Publication City/Country: Oxford
  • ISBN 10: 019956308X
  • ISBN 13: 9780199563081
  • Edition: 2, Revised
  • Edition statement: 2nd Revised edition
  • Illustrations note: 56 line illustrations
  • Sales rank: 260,555

Product description

One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as 'rubber-sheet geometry', with pictures of Mobius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

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Author information

Wilson A Sutherland was for many years a lecturer in mathematics in the University of Oxford, and a mathematics tutor at New College, Oxford. He has also taught at Massachusetts Institute of Technology and the University of Manchester, and, as a visiting professor, at Yale University and the University of Aberdeen.

Review quote

The presentation, description and explanation throughout the seventeen short chapters are excellent, and the text can be described as self-contained, with many suitably chosen examples and exercises ,.. An interesting innovation for the new edition is having a companion web site in which more useful and relevant materials can be found. Peter Shiu, The Mathematical Gazette

Table of contents

PREFACE ; 1. Introduction ; 2. Notation and terminology ; 3. More on sets and functions ; 4. Review of some real analysis ; 5. Metric spaces ; 6. More concepts in metric spaces ; 7. Topological spaces ; 8. Continuity in topological spaces; bases ; 9. Some concepts in topological spaces ; 10. Subspaces and product spaces ; 11. The Hausdorff condition ; 12. Connected spaces ; 13. Compact spaces ; 14. Sequential compactness ; 15. Quotient spaces and surfaces ; 16. Uniform convergence ; 17. Complete metric spaces ; REFERENCES ; INDEX