Introduction to Topology: Second Edition / Edition 2

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Overview


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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Editorial Reviews

Booknews
This introduction to topology employs a methodology somewhat different from other texts. Metric space and point-set topology material are treated in the first two chapters, and algebraic topological material is covered in the remaining two chapters, leading the reader through nontrivial applications of metric space topology to analysis. Treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proofs of some highly nontrivial results. Assumes familiarity with real numbers and some basic set theory. Includes chapter exercises. The authors are affiliated with UCLA. This is an unabridged republication of a work published by Saunders College Publishing, Philadelphia, 1983. This edition contains solutions to selected exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780486406800
  • Publisher: Dover Publications
  • Publication date: 2/16/1999
  • Series: Dover Books on Mathematics Series
  • Edition description: REV
  • Edition number: 2
  • Pages: 256
  • Sales rank: 960,097
  • Product dimensions: 6.15 (w) x 9.20 (h) x 0.48 (d)

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
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