Topology

Abstract

I. GENERAL TOPOLOGY. 1. Set Theory and Logic. 2. Topological Spaces and Continuous Functions. 3. Connectedness and Compactness. 4. Countability and Separation Axioms. 5. The Tychonoff Theorem. 6. Metrization Theorems and Paracompactness. 7. Complete Metric Spaces and Function Spaces. 8. Baire Spaces and Dimension Theory. II. ALGEBRAIC TOPOLOGY. 9. The Fundamental Group. 10. Separation Theorems in the Plane. 11. The Seifert-van Kampen Theorem. 12. Classification of Covering Spaces. 13. Classification of Surfaces.