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.