Topology
Metric Spaces-Definition and examples, Open spheres and Closed spheres, Open sets and Closed sets, Neighbourhood, Sequence in metric space. Continuous mapping and Completeness in metric space.
Topological Spaces-Definition and examples, Closed sets, Neighbourhood, Open base and sub base. Limit points, Adhere points and derived sets, Closure of a set, Subspaces, Continuity and Homeomorphism.
Compact and Locally Compact spaces, Connected and Locally connected spaces, Continuity and Compactness, Continuity and Connectedness,
Separation axioms: To 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, General product spaces.
- George F. Simmons, Introduction to Topology and Modern Analysis, Mcgraw Hill Book Company(2004).
- Colin Adams, Robert Franzosa, Introduction to Topology, parsons united edition press (2007).
- Dugundji,J,Topology,Prentice Hall of India,New Delhi,1975
- Munkers R James, A first course in Topology,Pearson Education Pvt. Ltd.,Delhi
- Terry Lawson, Topology: A Geometric Approach, Oxford University press (2003).
