PointSet Topology

Set theory, topological spaces, compactness, connectedness, separation properties, quotient spaces, Tychonoff Theorem, compactification, Urysohn Lemma and Tietze Extension Theorem, function spaces
Differential Topology

Smooth manifolds, transversality, Sard Theorem, matrix Lie groups, vector fields, PoincareHopf Theorem, differential forms, integration on manifolds, Stokes Theorem
Past Exams
Below are some MS Preliminary exams from previous years. They should give you an idea of the range of topics covered by the exams.





References
Lin and Lin: Set Theory
J.R. Munkres: Topology
Dugundji: Topology
V. Guillemin, A. Pollack: Differential Topology