Book:Ryszard Engelking/General Topology/Revised and Completed Edition

Ryszard Engelking: General Topology (Revised and Completed Edition)

Published $\text {1989}$, Heldermann

ISBN 3-88538-006-4

Subject Matter

• Topology

Contents

Preface to the first edition

Preface to the revised edition

Introduction

I.1 Algebra of sets. Functions

I.2 Cardinal numbers

I.3 Order relations. Ordinal numbers

I.4 The axiom of choice

I.5 Real numbers

Chapter 1: Topological spaces

1.1 Topological spaces. Open and closed sets. Bases. Closure and interior of a set

1.2 Methods of generating topologies

1.3 Boundary of a set and derived set. Dense and nowhere dense sets. Borel sets

1.4 Continuous mappings. Closed and open mappings. Homeomorphisms

1.5 Axioms of separation

1.6 Convergence in topological spaces: Nets and filters. Sequential and Fréchet spaces

1.7 Problems

Chapter 2: Operations on topological spaces

2.1 Subspaces

2.2 Sums

2.3 Cartesian products

2.4 Quotient spaces and quotient mappings

2.5 Limits of inverse systems

2.6 Function spaces I: The topology of uniform convergence on RX and the topology of pointwise convergence

2.7 Problems

Chapter 3: Compact spaces

3.1 Compact spaces

3.2 Operations on compact spaces

3.3 Locally compact spaces and $k$-spaces

3.4 Function spaces II: The compact-open topology

3.5 Compactifications

3.6 The Cech-Stone compactification and the Wallman extension

3.7 Perfect mappings

3.8 Lindelöf spaces

3.9 Cech-complete spaces

3.10 Countably compact spaces, pseudocompact spaces and sequentially compact spaces

3.11 Realcompact spaces

3.12 Problems

Chapter 4: Metric and metrizable spaces

4.1 Metric and metrizable spaces

4.2 Operations on metrizable spaces

4.3 Totally bounded and complete metric spaces. Compactness in metric spaces

4.4 Metrization theorems I

4.5 Problems

Chapter 5: Paracompact spaces

5.1 Paracompact spaces

5.2 Countably paracompact spaces

5.3 Weakly and strongly paracompact spaces

5.4 Metrization theorems II

5.5 Problems

Chapter 6: Connected spaces

6.1 Connected spaces

6.2 Various kinds of disconnectedness

6.3 Problems

Chapter 7: Dimension of topological spaces

7.1 Definitions and basic properties of dimensions ind, Ind, and dim

7.2 Further properties of the dimension dim

7.3 Dimension of metrizable spaces

7.4 Problems

Chapter 8: Uniform spaces and proximity spaces

8.1 Uniformities and uniform spaces

8.2 Operations on uniform spaces

8.3 Totally bounded and complete uniform spaces. Compactness in uniform spaces

8.4 Proximities and proximity spaces

8.5 Problems

Bibliography

Tables

Relations between main classes of topological spaces

Invariants of operations

Invariants and inverse invariants of mappings

List of special symbols

Author index

Subject index