Topology Qualifier Topics
Last revised: May 2011
I. General Topology:
- Basis for a Topology
- Product Topology (for finite product of spaces)
- Subspace Topology
- Metric Topology
- Quotient Topology
- Continuous Functions
- Connectedness
- Compactness
- Separation Axioms
II. Algebraic/Geometric Topology:
- Fundamental Group of a Space
- Covering Spaces
- Free Groups and Group Presentations
- Seifert-Van Kampen Theorem
- Fundamental Groups of Spheres, Surfaces, and 2-dimensional CW-complexes
- Retractions and Fixed Points
- Borsuk-Ulam Theorem
- Deformation Retracts and Homotopy Type
- Classification of Surfaces
- Classification and Construction of Covering Spaces
- Deck Transformations Groups and Discontinuous Group Actions on Spaces
- Lifting of Maps to Covering Spaces
- Fundamental Groups of Graphs, and Applications to Group Theory
- Simplicial Homology