Introduction to Topology

Topological spaces and continuous functions (product topology, quotient topology, metric topology). Connectedness and Compactness. Countabilty Axioms and Separation Axioms (the Urysohn lemma, the Urysohn metrization theorem, Partition of unity). The Tychonoff theorem and the Stone-Cech compactification. Metrization theorems and paracompactness.