Book:John L. Kelley/General Topology
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John L. Kelley: General Topology
Published $\text {1955}$, 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
Cited by
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.)
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces
Source work progress
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Algebraic Concepts
- Going around again. Closer look needed at the axioms underlying the definition of Ordering.