# Book:Bert Mendelson/Introduction to Topology/Third Edition

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## Bert Mendelson:

## Contents

## Bert Mendelson: *Introduction to Topology (3rd Edition)*

Published $\text {1975}$, **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**

## Further Editions

- 1962: Bert Mendelson:
*Introduction to Topology* - 1968: Bert Mendelson:
*Introduction to Topology*(2nd ed.)

## Source work progress

- 1962: Bert Mendelson:
*Introduction to Topology*... (previous) ... (next): $\S 3.3$: Neighborhoods and Neighborhood Spaces: Exercise $3$

- Got bogged down in Neighborhood Spaces, and I have basically skipped the exercises. Reworking, getting the edition correct:

- 1975: Bert Mendelson:
*Introduction to Topology*(3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 10$: Arbitrary Products: Exercise $1$

- Work needed on establishing rigorous definitions and understandable interpretations of a general cartesian product of a family of sets indexed by an uncountable set.

Revisit the following -- it has been glossed over:

- 1975: Bert Mendelson:
*Introduction to Topology*(3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 7$: Relations: Exercise $2$