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

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Ryszard Engelking: General Topology (Revised and Completed Edition)

Published $1989$, Heldermann

ISBN 3-88538-006-4.


Subject Matter


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