[Graduate Texts in Mathematics 27] • General Topology by Kelley, John L. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Preface Acknowledgments Contents 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