TOPOLOGY PRELIM REVIEW
Topology Prelim Topics
11 review lectures, June 3 to July 8, 2021
SAMPLE PROBLEMS (2021-22)
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