TOPOLOGY
Point-set topology: Open and closed sets, continuous functions, Metric topology, Product topology, Connectedness and path-connectedness, Compactness, Countability axioms, Separation axioms, Complete metric spaces, Quotient topology, Topological groups, Orbit spaces.
The fundamental group: Homotopic maps, Construction of the fundamental group, Fundamental group of the circle, Homotopy type, Brouwer’s fixed-point theorem, Separation of the plane. Recommended Books
- Armstrong, M. A., Basic Topology, Springer (India), 2004.
- Munkres, K. R., Topology,Pearson Education, 2005.
- Viro, O.Ya., Ivanov, O.A., Netsvetaev, N., and Kharlamov, V.M., Elementary Topology: Problem Textbook, AMS, 2008