MA 5040: Introduction to Topology

All updates related to MA 5040 are announced in the Google classroom.

### Class timings:

Monday: 12:00 noon to 13:00

Tuesday: 09:00 am to 10:00 am

Friday: 11:00 am to 11:55 am

### Examination and Grades:

The grades will be decided by the marks obtained in the assignments and the final examination.

## Syllabus:

Metric spaces, Topology, Opensets, Limit points, Closed sets, Interior points.

Continuous, Open and Closed maps, Homeomorphism.

Basis and subbasis of a topology, Separation axioms, Separability.

Subspace, Connectedness, Path connecetedness and local connectedness.

Compactness, local compactness, One point compactification.

Product space, Quotient space, Tychonoff's theorem, Lindelof space.

Urysohn's Lemma, Tietze extension theorem, Urysohn's metrization theorem.
## References:

- Croom, Fred H. Basic concepts of algebraic topology. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1978.
- Munkres, J. R. Topology: a first course. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1975.
- Joshi, K. D. Introduction to general topology. John Wiley & Sons, Inc., New York, 1983.
- Kelly, J. L. General topology. Graduate Texts in Mathematics, No. 27. Springer-Verlag, New York-Berlin, 1975.

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