Point Set Topology
Point Set Topology. Instructor: Prof. Ronnie Sebastian. Point set topology is one of the most important and basic courses that one encounters during a masters program in mathematics. This course introduces students to the most important concepts in point set topology. The course begins by defining topological spaces and introducing various ways to put topologies on sets. Then the notion of continuous maps is introduced. Continuous maps enable us to see how different topological spaces interact with each other. A very special class of topological spaces is metric spaces. Most of our intuition for topology comes from metric spaces. Metric spaces are introduced and we analyze the concepts developed so far in this special case. After this the topological properties of connectedness, compactness and local compactness are studied. Then another method to put a topology on a set, namely the quotient topology, is introduced. Finally the course ends with a discussion on when a topology arises from a metric. The main result in this part is Urysohn's Metrization Theorem. (from nptel.ac.in)
| Lecture 02 - Examples of Topological Spaces |
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