|Course Archives Theoretical Statistics and Mathematics Unit|
Course: Topology I
Time: Currently offered
Syllabus: Topological spaces, open and closed sets, basis, closure, interior and boundary. Subspace topology, Hausdorff spaces. Continuous maps: properties and constructions; Pasting Lemma. Homeomorphisms. Product topology, Quotient topology and examples of Topological Manifolds. Connected, path-connected and locally connected spaces. Lindelof and Compact spaces, Locally compact spaces, one-point compactification and Tychonoffs theorem. Paracompactness and Partitions of unity. Countability and separation axioms. Urysohns lemma, Tietze extension theorem and applications. Completion of metric spaces. Baire Category Theorem and applications. Time permitting, Urysohn embedding lemma and metrization theorem for second countable spaces. Covering spaces, Path Lifting and Homotopy Lifting Theorems, Fundamental Group.
1. J. R. Munkres, Topology: a first course, Prentice-Hall of India (2000).
2. K. Janich, Topology, UTM, Springer (Indian reprint 2006).
3. M.A. Armstrong, Basic Topology, Springer (Indian reprint 2004).
4. G.F. Simmons, Introduction to Topology and Modern Analysis, TataMcGraw- Hill (1963).
5. J.L. Kelley, General Topology, Springer (Indian reprint 2005).
6. I. M. Singer and J. A. Thorpe, Lecture Notes on Elementary Topology and Geometry, UTM, Springer (Indian reprint 2004).
7. J. Dugundji, Topology, UBS (1999).
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