Foundations of General Topology

PrefaceChapter 1 Algebra of Sets 1.1 Sets and Subsets 1.2 Operations on Sets 1.3 Relations 1.4 Mappings 1.5 Partial OrdersChapter 2 Cardinal and Ordinal Numbers 2.1 Equipotent Sets 2.2 Cardinal Numbers 2.3 Order Types 2.4 Ordinal Numbers 2.5 Axiom of ChoiceChapter 3 Topological Spaces Introduction 3.1 Open Sets and Limit Points 3.2 Closed Sets and Closure 3.3 Operators and Neighborhoods 3.4 Bases and Relative TopologiesChapter 4 Connectedness, Compactness, and Continuity 4.1 Connected Sets and Components 4.2 Compact and Countably Compact Spaces 4.3 Continuous Functions 4.4 Homeomorphisms 4.5 Arcwise ConnectivityChapter 5 Separation and Countability Axioms 5.1 T0- and T1-Spaces 5.2 T2-Spaces and Sequences 5.3 Axioms of Countability 5.4 Separability and Summary 5.5 Regular and Normal Spaces 5.6 Completely Regular SpacesChapter 6 Metric Spaces 6.1 Metric Spaces as Topological Spaces 6.2 Topological Properties 6.3 Hilbert (l2) Space 6.4 Fréchet Space 6.5 Space of Continuous FunctionsChapter 7 Complete Metric Spaces 7.1 Cauchy Sequences 7.2 Completions 7.3 Equivalent Conditions 7.4 Baire TheoremChapter 8 Product Spaces 8.1 Finite Products 8.2 Product Invariant Properties 8.3 Metric Products 8.4 Tichonov Topology 8.5 Tichonov TheoremChapter 9 Function and Quotient Spaces 9.1 Topology of Pointwise Convergence 9.2 Topology of Compact Convergence 9.3 Quotient TopologyChapter 10 Metrization and Paracompactness 10.1 Urysohn's Metrization Theorem 10.2 Paracompact Spaces 10.3 Nagata-Smirnov Metrization TheoremChapter 11 Uniform Spaces 11.1 Quasi Uniformization 11.2 Uniformization 11.3 Uniform Continuity 11.4 Completeness and Compactness 11.5 Proximity SpacesBibliographyIndex