MATH 440

Continuity, connectedness, and compactness are treated as basic concepts and developed for general topological spaces. The Tychonoff theorem, Urysohn's lemma and the Tietze extension theorem, together with applications, comprise about half the course. The topology of metric spaces, including paracompactness and the Baire category theorem, is developed. Problems for the written portion of the departmental qualifying exams are composed from the above material. If time permits, topics involving compactly generated topologies are discussed for use in homotopy theory. Some instructors may treat topics from algebraic topology like the fundamental group and covering spaces.

This page was last revised on July 29, 2002.