Details of MA3109 (Autumn 2022)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3109 | Topology and metric spaces | Arjun Paul |
| Syllabus |
|---|
| 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. |
| References |
|---|
| 1. 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. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MP | 1 | Core |
| 5 | MP | 3 | Not Allowed |
| 6 | MR | 1 | Not Allowed |
| 7 | MR | 3 | Not Allowed |
| 8 | MS | 3 | Not Allowed |
| 9 | MS | 5 | Not Allowed |
| 10 | MS | 7 | Not Allowed |
| 11 | MS | 9 | Not Allowed |
| 12 | RS | 1 | Not Allowed |
| 13 | RS | 2 | Not Allowed |