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Introduction To Topology 2ND Edition

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Introduction To Topology 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

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)

Synopsis:

Fresh approach explains nontrivial applications of metric space topology to analysis; topics from elementary algebraic topology focus on concrete results with minimal formalism. First two chapters: metric space, point-set topology; second two, algebraic topology. 1983 edition. Solutions to Selected Exercises. 51 illus.

Synopsis:

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 co

Synopsis:

This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Synopsis:

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. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Description:

Includes bibliographical references (p. 192) and index.

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

Product Details

ISBN:
9780486406800
Author:
Gamelin, Theodore W.
Author:
Greene, Robert Everist
Author:
Mathematics
Author:
Gamelin, Theodore W.
Publisher:
Dover Publications
Location:
Mineola, N.Y. :
Subject:
Topology
Subject:
Topology - General
Subject:
General Mathematics
Subject:
MATHEMATICS / Topology
Edition Number:
2
Edition Description:
Second Edition
Series:
Dover books on mathematics
Series Volume:
105-393
Publication Date:
19990231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
256
Dimensions:
8.5 x 5.38 in 0.76 lb

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Introduction To Topology 2ND Edition New Trade Paper
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Product details 256 pages Dover Publications - English 9780486406800 Reviews:
"Synopsis" by , Fresh approach explains nontrivial applications of metric space topology to analysis; topics from elementary algebraic topology focus on concrete results with minimal formalism. First two chapters: metric space, point-set topology; second two, algebraic topology. 1983 edition. Solutions to Selected Exercises. 51 illus.

"Synopsis" by , 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 co
"Synopsis" by ,
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
"Synopsis" by ,
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. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
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