MTL507: Topology

4 Credits (3-1-0)

Topological spaces: Definitions and Examples, Basis and Subbasis for a Topology, limit points, closure, interior; Continuous functions, Homeomorphisms; Subspace Topology, Metric Topology, Product & Box Topology, Order Topology; Quotient spaces.

Connectedness and Compactness: Connectedness, Path connectedness; Connected subspaces of the real line; Components and local connectedness; Compact spaces, Limit point compactness, Sequential compactness; Local compactness, One point compactification; Tychonoff theorem, characterizations of compact metric spaces. Countability Axioms: First countable spaces, Second countable spaces, Separable spaces, Lindeloff spaces.

Separation Axioms: Hausdorff, Regular and Normal spaces; Urysohn’s lemma; Uryohn’s Metrization theorem; Tietze extension theorem.

Completely metrizable spaces, Baire’s category theorem and Function Spaces.