Details of MA3201 (Spring 2013)
| Level: 3 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3201 | Topology | Sriram Balasubramanian |
| Syllabus |
|---|
| 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, local compactness; Tychonoff theorem, Stone-Weierstrass theorem. Separation Axioms : Hausdorff, regular and normal spaces; Urysohn lemma and Tietze extension theorem; compactification. Metrizability : Urysohn metrization theorem. Algebraic Topology : Fundamental groups, examples; covering spaces. |
| References |
|---|
| 1. Armstrong, M. A., Basic Topology, Undergraduate Texts in Mathematics, Springer-Verlag, 1983.
2. Dugundji, J., Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn & Bacon, 1978. 3. Kelley, J. L., General Topology, Graduate Texts in Mathematics, Springer-Verlag, 1975. 4. Munkres, J. R., Topology (2nd Edition), Prentice-Hall, 2000. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP ( Mathematical Sciences ) | 2 | Core |
| 2 | IP | 4 | Not Allowed |
| 3 | MS ( Mathematical Sciences ) | 6 | Core |
| 4 | RS | 1 | Elective |