Book:John L. Kelley/General Topology

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John L. Kelley: General Topology

Published $1955$, D. Van Nostrand Company, Inc.

ISBN 0387901256.


Subject Matter


Contents

Preface
Acknowledgments
Chapter 0: Preliminaries
Sets
Subsets and Complements; Union and Intersection
Relations
Functions
Orderings
Algebraic Concepts
The Real Numbers
Countable Sets
Cardinal Numbers
Ordinal Numbers
Cartesian Products
Hausdorff Maximal Principle
Chapter 1: Topological Spaces
Topologies and Neighborhoods
Closed Sets
Accumulation Points
Closure
Interior and Boundary
Bases and Subbases
Relativization; Separation
Connected Sets
Problems
Chapter 2: Moore-Smith Convergence
Introduction
Directed Sets and Nets
Subnets and Cluster Points
Sequences and Subsequences
$^*$Convergence Classes
Problems
Chapter 3: Product and Quotient Spaces
Continuous Functions
Product Spaces
Quotient Spaces
Problems
Chapter 4: Embedding and Metrization
Existence of Continuous Functions
Embedding in Cubes
Metric and Pseudo-Metric Spaces
Metrization
Problems
Chapter 5: Compact Spaces
Equivalences
Compactness and Separation Properties
Products of Compact Spaces
Locally Compact Spaces
Quotient Spaces
Compactification
Lebesgue's Covering Lemma
$^*$Paracompactness
Problems
Chapter 6: Uniform Spaces
Uniformities and the Uniform Topology
Uniform Continuity; Product Uniformities
Metrization
Completeness
Completion
Compact Spaces
For Metric Spaces Only
Problems
Chapter 7: Function Spaces
Pointwise Convergence
Compact Open Topology and Joint Continuity
Uniform Convergence
Uniform Convergence on Compacta
Compactness and Equicontinuity
$^*$Even Continuity
Problems
Appendix: Elementary Set Theory
Classification Axiom Scheme
Classification Axiom Scheme (Continued)
Elementary Algebra of Classes
Existence of Sets
Ordered Pairs; Relations
Functions
Well Ordering
Ordinals
Integers
The Choice Axiom
Cardinal Numbers
Bibliography
Index