Topology Syllabus (for MS and Preliminary Exams)

Point-Set 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, Poincare-Hopf 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.

June 2007
August 2007
June 2008
August 2008
June 2009
August 2009
June 2010
June 2011
August 2011
June 2013
August 2013
August 2017
June 2021


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