Foundations of General Topology

TABLE OF CONTENTS: CHAPTER 1. Algebra of Sets -- 1.1 Sets and Subsets -- 1.2 Operations on Sets -- 1.3 Relations -- 1.4 Mappings -- 1.5 Partial Orders --------- CHAPTER 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 Choice --------- CHAPTER 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 Topologies --------- CHAPTER 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 Connectivity --------- CHAPTER 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 Spaces --------- CHAPTER 6. Metric Spaces -- 6.1 Metric Spaces as Topological Spaces -- 6.2 Topological Properties -- 6.3 Hilbert (I2) Space -- 6.4 Frechet Space -- 6.5 Space of Continuous Functions --------- CHAPTER 7. Complete Metric Spaces -- 7.1 Cauchy Sequences. 7.2 Completions 7.3 Equivalent Conditions -- 7.4 Baire Theorem --------- CHAPTER 8. Product Spaces -- 8.1 Finite Products -- 8.2 Product Invariant Properties -- 8.3 Metric Products -- 8.4 Tichonov Topology -- 8.5 Tichonov Theorem --------- CHAPTER 9. Function and Quotient Spaces -- 9.1 Topology of Pointwise Convergence -- 9.2 Topology of Compact Convergence -- 9.3 Quotient Topology --------- CHAPTER 10. Metrization and Paracompactness -- 10.1 Urysohn's Metrization Theorem -- 10.2 Paracompact Spaces