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# 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

3 The real line

4 Products of metric spaces

8 The contraction principle

9 The Frechet derivative

TWO TOPOLOGICAL SPACES

10 Finite product spaces

11 Set theory and Zorn's lemma

THREE HOMOTOPY THEORY

1 Groups

3 The fundamental group

6 Some applications of the index

8 Maps into the punctured plane

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