27008 - General Topology
1.- METRIC SPACES (I): Normed linear spaces. Metric spaces. Limit point, Derived and Closure set. Open sets.
2.- TOPOLOGICAL SPACES: Topological spaces. Bases and subbases. Interior, derived set, clousure and frontier.
3.- CONTINUOUS FUNCTIONS: Relative topology and subspaces. Open and closed maps, homeomorphisms. Product spaces. Quotient spaces.
4.- SEPARATION AND COUNTABILITY: Hausdorff spaces. Regular spaces. Normal spaces. Countability properties and related concepts.
5.- COMPACTNESS: Compact spaces. Locally compact spaces. Alexandroff compactification. Countably and sequentally compact spaces.
6.- METRIC SPACES (II): Compactness in metric spaces. Complete metric spaces. Completion of a matric space.
7.- CONNECTEDNESS: Connected spaces. Locally connectes spaces. Pathwise connected spaces. The homotopy relation.
8.- HOMOGENEOUS SPACES: Topological groups. Topological transformations groups. Topology of linear groups.