Topology [MAL6010] (3 Credits)
Monday, Wednesday , Friday (8:00- 8:55 AM)
Internal -40 %
Quizzes- 40% (Best Four out of five quizzes with equal weightage)
External-60%
Mid semester Examination I - 15%
Mid semester Examination II -15%
End semester Examination - 30%
The Quizzes will be conducted on August 20, September 14, October 7, October 28 and November 9,2022.
Basic Topology : Topological spaces, basis and sub-basis, order topology, product topology, subspace topology, closed sets, limit points, continuous functions, quotient topology
Properties of Topological Spaces : Connected spaces, Components, local connectedness, compact spaces, limit point compactness, local compactness, Countability axioms, separation axioms, normal spaces, Tychonoff spaces, Urysohn’s metrization theorem, Tietze extension theorem, Tychonoff theorem, Stone-Cech compactification
Special Topics : Function spaces, pointwise and uniform convergence, compactopen topology, uniform convergence on compact set, Stone-Weierstrass Theorem.
Munkres, J., Topology, second edition, Pearson Publications, 2000
Willard, S., General Topology, Dover Publications, 2004
Pervin, W. J. and Boas, R. P., Foundations of general topology, Academic Press, 1964
Simmons, G. F., Introduction to topology and modern analysis, Tata McGraw-Hill, 2004