Topological spaces – Basis for a topology - The Order Topology – Product Topology on X x Y – The subspace topology - Closed sets and Limit Points .
Continuous Functions – Product Topology - Metric Topology.
Connected Spaces – Connected subspaces of the real line – Components and Local Conne
Compact Spaces Compact subspaces of the real line – Limit Point Compactness.
The Countability Axioms – The Separation Axioms - The Urysohn Lemma – Urysohn Metrization Theorem
Reference Book:
Reference Books: 1. Introduction to Topology and Modern Analysis by George F. Simmons, McGraw Hill Book Company, 1963. 2. General Topology by J.L. Kelley, Third Indian Reprint 2012, Springer
Text Book:
Topology, A First Course by James R. Munkres, Prentice Hall of India Private Limited, New Delhi, 2011, Second Edition. Unit-I: Chapter 2: Sections 12 – 17. Unit-II: Chapter 2: Sections 18-20. Unit-III: Chapter 3: Sections 23 – 25. Unit-IV: Chapter 3: Sections 26 – 28. Unit-V: Chapter 4: Sections 30, 31, 33, 34.
