Course

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.

1. J. Munkres, “Topology”; Prentice Hall, 2002, Second edition
2. S. Kumaresan, “Topology of Metric Spaces”; Narosa Publishing House, New Delhi, 2011Second Reprint. 
3. J. Dugundji, “ Topology” Allyn and Bacon, Boston-1966.
4. Fred H. Croom, “Principles of Topology”, Cengage Learning.