Course information

Basic notions: Topological spaces, Basis, subbasis of topology, Open sets, closed sets, closure, interior, boundary, continuous functions, relative topology, homeomorphisms. Cartesian products: Product topology, projections, general properties. Connectedness: Definitions, properties, Connective components; Path connectedness, Applications to R^n. Separation axioms: Hausdorff spaces, regular spaces, normal spaces, completely regular spaces. Countability and Metrizable topological spaces. Separability. First and second countable spaces, Lindelof spaces, Urysohn’s metrizability Theorem. Compactness: Tychonoff’s Theorem, Stone Cech compactification, Superfilters, the space N. Convergence: Convergence in topological spaces, nets, subnets.