Topology

Code: MA549 | L-T-P-C: 3-1-0-8

Prerequisites: MA541 Real Analysis

Topological spaces, Bases and sub-bases for a topology, Limit point, closure, interior, boundary of a set, dense and nowhere dense sets, Continuity, Homeomorphism, Subspace, Product and Quotient topologies. Countability axioms, Separation axioms. Connectedness; Components, path connectedness, locally connected spaces, totally disconnected spaces. Compactness; Tychonoff’s theorem, locally compact spaces, one-point compactification. Urysohn’s lemma, Tietze’s extension theorem, Urysohn’s metrization theorem.

Texts:

1. J. R. Munkres: Topology, Pearson India, 2015.

References:

1. C. W. Patty, Foundations of Topology, Second Edition, Jones & Barlett Student Edition, 2010.
2. G. F. Simmons: Introduction to Topology and Modern Analysis, McGraw-Hill India, 2017
3. S. Willard: General Topology, Dover, 2004.