Topological Spaces: Definition and examples, Closed sets, Neighborhood, Open base and sub base, Limit points, Adhere points and derived sets, Closure of a set.
Subspaces, Continuity and homeomorphism, Nets, Filters.
Compact and locally compact spaces Connected and locally connected spaces, Continuity and compactness, Continuity and connectedness.
Separation axioms: T0 space, T1 space, T2 space or Hausdroff space, Regular and T3 spaces, Normal and T4 spaces.
Product spaces: Product space of two spaces, Product invariant properties for finite products, Quotient spaces.
1. George F. Simmons, Introduction to Topology and Modern Analysis, McGraw Hill , 2004.
2. Colin Adams, Robert Franzosa, Introduction to Topology, Pearsons united edition press, 2007.
3. K.D.Joshi, Introduction to General Topology, Wiley Eastern Ltd., 1983.
1. Dugundji. J, Topology, Prentice Hall of India, New Delhi, 1975.
2. Munkers R James, A first Course in Topology,Pearson Education Pvt. Ltd. Delhi, 2015.
3. Terry Lawson, Topology: A Geometric Approach, Oxford University press, 2003.
4. I.M. Singer and J. Thorpe, Lecture notes on Elementary Topology and Geometry, Springer, 1967.
5. Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002.
6. W.J. Pervn, Foundation of General Topology, Academic Press Ltd., 1996.
7. M.G. Murdeshevar, Topology, Wiley Eastern Ltd, 1983.
Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/topology
[2] https://maths.iisuniv.ac.in/academic-year/2018-2019