Details of MA3201 (Spring 2015)

Level: 6 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA3201 Topology Sriram Balasubramanian,
Swarnendu Datta

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. M. A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer-Verlag, 1983.

  2. J. Dugundji, Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn & Bacon, 1978.

  3. J. L. Kelley, General Topology, Graduate Texts in Mathematics, Springer-Verlag, 1975.

  4. J. R. Munkres, Topology (2nd Edition), Prentice Hall, 2000.


Course Credit Options

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