Modern General Topology

Chapter I Introduction 1. Set 2. Cardinal Numbers 3. Ordinal Numbers 4. Zermelo's Theorem and Zorn's Lemma 5. Topology of Euclidean Plane Exercise IChapter II Basic Concepts in Topological Spaces 1. Topological Space 2. Open Basis and Neighborhood Basis 3. Closure 4. Convergence 5. Covering 6. Mapping 7. Subspace, Product Space, Quotient Space and Inverse Limit Space 8. Connectedness Exercise IIChapter III Various Topological Spaces 1. T1, Τ2, Regular and Completely Regular Spaces 2. Normal Space and Fully Normal Space 3. Compact Space and Paracompact Space 4. Axioms of Countability 5. Metric Space Exercise IIIChapter IV Compact Spaces and Related Topics 1. Product of Compact Spaces 2. Compactification 3. Compact Space and the Lattice of Continuous Functions 4. Extensions of the Concept of Compactness Exercise IVChapter V Paracompact Spaces and Related Topics 1. Fundamental Theorem 2. Further Properties of Paracompact Spaces 3. Countably Paracompact Space 4. Modifications of the Concept of Paracompactness 5. Characterization by Product Spaces Exercise VChapter VI Metrizable Spaces and Related Topics 1. Metrizability 2. Imbedding 3. Union and Image of Metrizable Spaces 4. Uniform Space 5. Proximity Space 6. P-Spaces Exercise VIChapter VII Topics Related to Mappings 1. Mapping Space 2. Metric Space, Paracompact Space and Continuous Mapping 3. Theory of Inverse Limit Space 4. Theory of Selection Exercise VIIEpilogueBibliographyIndex