Introduction to Topology by Gamelin and Greene

Introduction to Topology by Theodore W. Gamelin, Robert Everist Greene

Used it once as the textbook for Introductory algebraic topology: course.

Could use more pictures. Proofs can be more gentle, details, less "compact".

Overall, a good book.

Cheap.

Contents

ONE METRIC SPACES

1 Open and closed sets

2 Completeness

3 The real line

4 Products of metric spaces

5 Compactness

6 Continuous functions

7 Normed linear spaces

8 The contraction principle

9 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 spaces

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