Topology

3 Credits · Level: Graduate, Undergraduate

This course serves as an introduction to topology, both point-set topology and algebraic topology. The first half of the course is devoted to the basics of point-set topology. Topics include topological spaces, basis for a topology, metric spaces, subspaces, product spaces, continuous maps and homeomorphisms, connectedness and path-connectedness, compactness, the Cantor set, quotient spaces, and surfaces. The remainder of the course explores some aspects of algebraic topology: homotopy and homotopy type, cell complexes, operations on spaces, homotopy equivalence, the fundamental group and its applications, Van Kampen's theorem, and covering spaces.