Topology Prelim Topics

11 review lectures, June 3 to July 8, 2021


Review set 1  Countability properties (13 problems)

Review set 2  Separation properties, existence of continuous functions (11 problems)

Review Set 3  Metric spaces: G-delta sets, Baire property, Heine-Borel spaces (12 problems)

Review Set 4  Compactness, local compactness, Alexandroff compactification, proper maps (28 problems)

Review Set 5  Topologies on spaces of maps/Arzela-Ascoli/Stone-Weierstrass (22 problems)

Review Set 6  Connected spaces (14 problems)

Review Set 7  Differentiable manifolds: immersions, submersions, embedding, stability, Sard's theorem (27 problems)

Review Set 8  Topological applications of differentiable techniques (35 problems)

List 8-some solutions

Review Set 9  Fundamental group and covering spaces (38 problems)

List 9-some solutions