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

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

Published $1999$, Dover Publications

ISBN 0-486-40680-6.


Subject Matter


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