# Book:Bert Mendelson/Introduction to Topology

## Bert Mendelson: *Introduction to Topology*

Published $1962$, **Dover Publications, Inc.**

- ISBN 0-486-66352-3.

### Subject Matter

### Contents

*Preface to Third Edition*

**$1 \quad$ Theory of Sets**

*1 Introduction**2 Sets and subsets**3 Set operations: union, intersection, and complement**4 Indexed families of sets**5 Products of sets**6 Functions**7 Relations**8 Composition of functions and diagrams**9 Inverse functions, extensions and restrictions**10 Arbitrary products*

**$2 \quad$ Metric Spaces**

*1 Introduction**2 Metric spaces**3 Continuity**4 Open balls and neighborhoods**5 Limits**6 Open sets and closed sets**7 Subspaces and equivalence of metric spaces**8 An infinite dimensional Euclidean space*

**$3 \quad$ Topological Spaces**

*1 Introduction**2 Topological spaces**3 Neighborhoods and neighborhood spaces**4 Closure, interior, boundary**5 Functions, continuity, homeomorphism**6 Subspaces**7 Products**8 Identification of topologies**9 Categories and functors*

**$4 \quad$ Connectedness**

*1 Introduction**2 Connectedness**3 Connectedness on the real line**4 Some applications of connectedness**5 Components and local connectedness**6 Path-connected topological spaces**7 Homotopic paths and the fundamental group**8 Simple connectedness*

**$5 \quad$ Compactness**

*1 Introduction**2 Compact topological spaces**3 Compact subsets of the real line**4 Products of compact spaces**5 Compact metric spaces**6 Compactness and the Bolzano-Weierstrass property**7 Surfaces by identification*

**Bibliography**

**Index**