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Introduction To Topology 2ND Editionby Theodore Gamelin
Synopses & ReviewsPublisher 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 pointset 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 pointset 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, pointset 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, pointset 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 pointset 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 ContentsONE 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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