Topology

Course content

Topological spaces. Neighborhoods. Basis. Subspace topology, product and quotient topologies. Compactness. Tychonoff's Theorem. Heine-Borel theorem. Separation properties. Urysohn's Lemma and Tietze Extension theorem. Stone-Cech compactification. Alexandroff one point compactification. Convergence of sequences and nets. Connectedness. Metrizability. Complete metric spaces. Baire's theorem.