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

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