Introduction to Topology: Second Edition / Edition 2

Introduction to Topology: Second Edition / Edition 2

by Theodore W. Gamelin, Robert Everist Greene, Mathematics
     
 

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ISBN-10: 0486406806

ISBN-13: 9780486406800

Pub. Date: 02/16/1999

Publisher: Dover Publications


One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.
While there are many other works on introductory topology, this volume employs a methodology somewhat different from other

Overview


One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.
While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two. The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the 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 proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, important applications become immediately evident without the necessity of a large formal program.
Prerequisites are familiarity with real numbers and some basic set theory. Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition), while a list of notations and bibliographical references appear at the end of the book.

Product Details

ISBN-13:
9780486406800
Publisher:
Dover Publications
Publication date:
02/16/1999
Series:
Dover Books on Mathematics Series
Edition description:
REV
Pages:
256
Sales rank:
392,412
Product dimensions:
6.15(w) x 9.20(h) x 0.48(d)

Related Subjects

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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