Introduction to Metric and Topological Spaces

Paperback | July 15, 2009

byWilson A. Sutherland

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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 someof 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, firstin 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 thisfits 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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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 someof that influence. The aim is to move grad...

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.
Format:PaperbackDimensions:224 pages, 9.21 × 6.14 × 0.68 inPublished:July 15, 2009Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019956308X

ISBN - 13:9780199563081

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Table of Contents

Preface1. Introduction2. Notation and terminology3. More on sets and functions4. Review of some real analysis5. Metric spaces6. More concepts in metric spaces7. Topological spaces8. Continuity in topological spaces; bases9. Some concepts in topological spaces10. Subspaces and product spaces11. The Hausdorff condition12. Connected spaces13. Compact spaces14. Sequential compactness15. Quotient spaces and surfaces16. Uniform convergence17. Complete metric spacesReferencesIndex

Editorial Reviews

"...a carefully written introduction... a good, informative, well organized book..." --Jahresbericht der Deutschen Mathematiker-Vereinigung