The Metric Topology, The Countability Axioms, The Separation Axioms. Normal Spaces. The Urysohn Lemma, The Urysohn Metrization Theorem, The Tietze Extension Theorem. The Tychonoff Theorem, Local Finiteness, The Nagata-Smirnov Metrization Theorem,Para-compactness, The Smirnov Metrization Theorem. Complete Metric Spaces, Compactness in Metric Spaces, Pointwise and Compact Convergence, Ascoli’s Theorem, Baire Space. Homotopy of Paths, The Fundamental Group, Covering Spaces.

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4. Fred H. Croom, “Principles of Topology”, Cengage Learning.