Topology

(Last revised: May 2011)

Topology Qualifier Topics
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