MTL507
| MTL507 | |
|---|---|
| Topology | |
| Credits | 4 |
| Structure | 3-1-0 |
| Pre-requisites | |
| Overlaps | |
MTL507 : Topology
[edit]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.