Book:Theodore W. Gamelin/Introduction to Topology/Second Edition

Theodore W. Gamelin and Robert Everist Greene: Introduction to Topology (2nd Edition)

Published $\text {1999}$, Dover Publications

ISBN 0-486-40680-6

Subject Matter

• Topology

Contents

Preface

ONE: METRIC SPACES

1. Open and closed sets

2. Completeness

3. The real line

4. Products of metric spaces

5. Continuous functions

6. Normed linear spaces

7. The contraction principle

8. 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 spacs

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 $S^n$

3. Simplexes and barycentric subdivision

4. Approximation by piecewise linear maps

5. Degrees of maps

BIBLIOGRAPHY

LIST OF NOTATIONS

SOLUTIONS TO SELECTED EXERCISES

INDEX

Next

Further Editions

• 1983: Theodore W. Gamelin and Robert Everist Greene: Introduction to Topology

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