An invitation to Topology

Por: Swayam . en: ,

Week 1:Set theory and Logic: Sets and functions, Finite and Infinite sets, Well-ordered sets, Zorn’s lemma and the Axiom of ChoiceWeek 2:Topological spaces: the basic axioms of topology with examples, Bases and Subbases, Various kinds of topologies on the real lineWeek 3:Limit points and closed sets, continuous functionsWeek 4:Product topology, Quotient topology and Metric topologyWeek 5:Connectedness: connected spaces and subspaces, Connectedness of the real line, Intermediate value theoremWeek 6:Connected components, Path connected, locally connected, and locally path-connected spacesWeek 7:Compact spaces: open cover characterization, Finite intersection property, various notions of compactnessWeek 8:Compact subspaces of the real line, Heine-Borel theorem, extreme value theoremWeek 9:Urysohn’s Lemma and Tietze extension theorem on metric spacesWeek 10:Complete metric spaces, Totally bounded metric spaces and compactness, Lebesgue number lemmaWeek 11:Function spaces and the Arzela-Ascoli theoremWeek 12:Baire spaces and the Baire category theorem