Topology

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Overview

This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures.

GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory.

For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

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Product Details

  • ISBN-13: 9780131784499
  • Publisher: Pearson Prentice Hall
  • Publication date: 7/28/2003

Table of Contents

Preface
A Note to the Reader
Pt. I General Topology
Ch. 1 Set Theory and Logic 3
Ch. 2 Topological Spaces and Continuous Functions 75
Ch. 3 Connectedness and Compactness 147
Ch. 4 Countability and Separation Axioms 189
Ch. 5 The Tychonoff Theorem 230
Ch. 6 Metrization Theorems and Paracompactness 243
Ch. 7 Complete Metric Spaces and Function Spaces 263
Ch. 8 Baire Spaces and Dimension Theory 294
Pt. II Algebraic Topology
Ch. 9 The Fundamental Group 321
Ch. 10 Separation Theorems in the Plane 376
Ch. 11 The Seifert-van Kampen Theorem 407
Ch. 12 Classification of Surfaces 446
Ch. 13 Classification of Covering Spaces 477
Ch. 14 Applications to Group Theory 501
Bibliography 517
Index 519
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  • Anonymous

    Posted December 16, 2000

    A Very Classic Textbook in the subject

    This second edition is an overwhelming victory over not only most other textbooks in this realm of mathematics but also over its predecessor first edition. What distinguishes this textbook from others is that there is a clear boundary set forth between the contents in general topology and algebraic topology as well as the lucid exposition of the abstract concepts encountered in topology. With a more thorough coverage of the subject, this second edition brings even more delightful surprises to anyone both ardent and serious about exploring the abstract realm of advanced mathematics!! I definitely keep this book along with the first edition that I had used for my first course in topology!

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