Course Archives    Theoretical Statistics and Mathematics Unit
Course: Topology I
Instructor: Ramesh Sreekantan
Room: G25
Level: Postgraduate
Time: Currently offered
Syllabus
Past Exams


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.

Suggest Texts:
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).

Evaluation:
Midterm Exam 40 marks
Assignment 10 marks
Final Exam 50 marks
Total 100 marks


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Past Exams
Midterm
09.pdf 10.pdf 12.pdf 14.pdf 16.pdf 18.pdf
Semestral
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
Supplementary and Back Paper
04.pdf 06.pdf 10.pdf 14.pdf 16.pdf

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