21-651 General Topology

12 units, Carnegie Mellon University

Metric spaces: continuity, compactness, Arzela-Ascoli Theorem, completeness and completion, Baire Category Theorem. General topological spaces: bases and subbases, products, quotients, subspaces, continuity, topologies generated by sets of functions, homeomorphisms. Convergence: nets, filters, and the inadequacy of sequences. Separation: Hausdorff spaces, regular spaces, completely regular spaces, normal spaces, Urysohn's Lemma, Tietze's Extension Theorem. Connectedness. Countability conditions: first and second countability, separability, Lindelof property. Compactness: Tychonoff's Theorem, local compactness, one-point compactification. (Three 50 minute lectures)

Prerequisites: (21-355 (min B) or 21-235 (min B) or 21-455 (min B)) and (21-373 (min B) or 21-237 (min B))

Offered: Fall 2026, Fall 2025

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