Introduction to Topology

Introduction to Topology

Paperback Dover Books on Mathematics

By (author) T. W. Gamelin, By (author) Robert E. Greene

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  • Publisher: Dover Publications Inc.
  • Format: Paperback | 256 pages
  • Dimensions: 152mm x 229mm x 15mm | 159g
  • Publication date: 30 September 1999
  • Publication City/Country: New York
  • ISBN 10: 0486406806
  • ISBN 13: 9780486406800
  • Edition: 2, Revised
  • Edition statement: 2nd Revised edition
  • Sales rank: 283,389

Product description

A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.

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Table of contents

ONE METRIC SPACES   1 Open and closed sets   2 Completeness   3 The real line   4 Products of metric spaces   5 Compactness   6 Continuous functions   7 Normed linear spaces   8 The contraction principle   9 The Frechet derivative TWO TOPOLOGICAL SPACES   1 Topological spaces   2 Subspaces   3 Continuous functions   4 Base for a topology   5 Separation axioms   6 Compactness   7 Locally compact spaces   8 Connectedness   9 Path connectedness   10 Finite product spaces   11 Set theory and Zorn's lemma   12 Infinite product spaces   13 Quotient spaces THREE HOMOTOPY THEORY   1 Groups   2 Homotopic paths   3 The fundamental group   4 Induced homomorphisms   5 Covering spaces   6 Some applications of the index   7 Homotopic maps   8 Maps into the punctured plane   9 Vector fields   10 The Jordan Curve Theorem FOUR HIGHER DIMENSIONAL HOMOTOPY   1 Higher homotopy groups   2 Noncontractibility of Sn   3 Simplexes and barycentric subdivision   4 Approximation by piecewise linear maps   5 Degrees of maps   BIBLIOGRAPHY   LIST OF NOTATIONS   SOLUTIONS TO SELECTED EXERCISES   INDEX