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MA5040: Topology

(Possible) Syllabus :

Topological Spaces: open sets, closed sets, neighbourhoods, bases and sub bases, limit points, closures, interiors, continuous functions, homeomorphisms. Examples: order topology, subspace topology, product topology, metric topology, quotient topology. Connected spaces, Components and local connectedness. Compact spaces, Heine-Borel Theorem, Limit point compactness, and Local-compactness. The countability axioms. Hausdorff spaces, regular, completely regular, and normal spaces, Urysohn Lemma, Urysohn Metrization Theorem, Tietze Extension Theorem. Tychnoff Theorem, Stone-Cech Compactification. Complete metric spaces, compact metric spaces, equicontinuity, Ascoli's Theorem, Baire Category Theorem and its applications.
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  • Problems sheets: Some interesting stuffs: