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Edition: 2ND 00

Copyright: 2000

Publisher: Prentice Hall, Inc.

Published: 2000

International: No

Copyright: 2000

Publisher: Prentice Hall, Inc.

Published: 2000

International: No

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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.

**I. GENERAL TOPOLOGY.**

1. Set Theory and Logic.

2. Topological Spaces and Continuous Functions.

3. Connectedness and Compactness.

4. Countability and Separation Axioms.

5. The Tychonoff Theorem.

6. Metrization Theorems and Paracompactness.

7. Complete Metric Spaces and Function Spaces.

8. Baire Spaces and Dimension Theory.

**II. ALGEBRAIC TOPOLOGY.**

9. The Fundamental Group.

10. Separation Theorems in the Plane.

11. The Seifert-van Kampen Theorem.

12. Classification of Surfaces.

13. Classification of Covering Spaces.

14. Applications to Group Theory.

Index.

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Summary

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.

Table of Contents

**I. GENERAL TOPOLOGY.**

1. Set Theory and Logic.

2. Topological Spaces and Continuous Functions.

3. Connectedness and Compactness.

4. Countability and Separation Axioms.

5. The Tychonoff Theorem.

6. Metrization Theorems and Paracompactness.

7. Complete Metric Spaces and Function Spaces.

8. Baire Spaces and Dimension Theory.

**II. ALGEBRAIC TOPOLOGY.**

9. The Fundamental Group.

10. Separation Theorems in the Plane.

11. The Seifert-van Kampen Theorem.

12. Classification of Surfaces.

13. Classification of Covering Spaces.

14. Applications to Group Theory.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2000

International: No

Published: 2000

International: No

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.

**I. GENERAL TOPOLOGY.**

1. Set Theory and Logic.

2. Topological Spaces and Continuous Functions.

3. Connectedness and Compactness.

4. Countability and Separation Axioms.

5. The Tychonoff Theorem.

6. Metrization Theorems and Paracompactness.

7. Complete Metric Spaces and Function Spaces.

8. Baire Spaces and Dimension Theory.

**II. ALGEBRAIC TOPOLOGY.**

9. The Fundamental Group.

10. Separation Theorems in the Plane.

11. The Seifert-van Kampen Theorem.

12. Classification of Surfaces.

13. Classification of Covering Spaces.

14. Applications to Group Theory.

Index.