Book:John L. Kelley/General Topology

Subject Matter

 * Topology
 * Metric Spaces
 * Set Theory
 * Uniform Spaces

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



Source work progress
* : Chapter $0$: Algebraic Concepts


 * Going around again. Refactoring needed around Image and Preimage of Subset under Mapping, as well as a closer look at the axioms underlying the definition of Ordering.


 * Vector spaces need to be reviewed also.