MAT 2026: Metric and Topological Spaces

Syllabus:  Metric spaces, open and closed sets. Euclidean spaces, normed linear spaces, examples of different normed linear spaces, sequence spaces. Completeness, Baire category Theorem. Compactness, characterization of compact spaces. Product spaces, Tychonoff’s theorem. Continuous functions, equicontinuous families, Arzela-Ascoli Theorem.  Connectedness, path connectedness.

General topological spaces, separation axioms. Hausdorff spaces. Convergence of nets.

Prerequisites: Calculus, Real Analysis, Linear algebra.

Desirable: Multivariable Calculus.

References:

1. M. O. Searcoid: Metric Spaces, Springer, 2007.
2. G. F. Simmons: Introduction to topology and modern analysis, Krieger Publishing, 2003.
3. S. Shirali and H. L. Vasudeva:  Metric Spaces, Springer, 2006.
4. J. R. Munkres: Topology, Pearson, 2^nd edition, 2000.