Book:Bert Mendelson/Introduction to Topology

Bert Mendelson: Introduction to Topology

Published $1962$, Dover Publications, Inc.

ISBN 0-486-66352-3.

Subject Matter

• Topology

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