Topological spaces and continuous functions:Topological spaces, Basis for a topology, Order topology, Product topology, Subspace topology, Closed sets and limit points, Continuous functions, Homeomorphism, Metric topology, Quotient topology.

Connectedness and compactness: Hausdorff spaces, Connected spaces, Connected subspaces of the real line, Compactness and local connectedness, Compact spaces, Compact subspaces of the real line, Tychonoff Theorem, Limit point compactness, Local compactness, Compactification, One-point compactification, Stone-Cech compactification.

Countability and separation axioms: Countability axioms, Separation axioms, Normal spaces, Regular spaces, Completely regular spaces, Urysohn lemma, Urysohn metrization theorem, Tietze extension lemma.

J. R. Munkres, Topology, Pearson Prentice Hall, 2005.

J. L. Kelley, General Topology, Van Nostrand, 1995.

G. F. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill, 1963