# 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