Details of MA3201 (Spring 2020)

Level: 3 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA3201 Topology Soumalya Joardar

Metric Spaces: Metric space topology, equivalent metrics, sequences, complete metric spaces, limits and continuity, uniform continuity, extension of uniformly continuous functions.

Topological Spaces: Definition, examples, bases, sub-bases, product topology, subspace topology, metric topology, quotient topology, second countability and separability.

Continuity: Continuous functions on topological spaces, homeomorphisms.

Connectedness: Definition, example, path connectedness and local connectedness.

Compactness: Definition, limit point compactness, sequential compactness, net and directed set, local compactness, Tychonoff theorem, Stone-Weierstrass theorem, Arzela-Ascoli theorem.

Topological Groups: Definitions, examples, compactness and connectedness in matrix groups.

Separation Axioms: Hausdorff, regular and normal spaces; Urysohn lemma and Tietze extension theorem; compactification.

Metrizability: Urysohn metrization theorem.

Analysis III (MA3101) and Algebra I (MA3102).

. Armstrong, M.A., Basic Topology, Springer-Verlag

2. Dugundji, J., Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn & Bacon.

3. Kelley, J.L., General Topology, Springer-Verlag.

4. Munkres, J.R., Topology (2nd Edition), Prentice-Hall.

5 Simmons, G.F., Introduction to Topology and Modern Analysis, Tata McGraw-Hill

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Core
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 6 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed