21-465 Topology

9 units, Carnegie Mellon University

Metric spaces. Topological spaces. Separation axioms. Open, closed and compact sets. Continuous functions. Product spaces, subspaces, quotient spaces. Connectedness and pathconnectedness. Homotopy. Fundamental group of a pointed space. Simply connected spaces. Winding number, the fundamental group of the circle. Functorial property of the fundamental group. Brouwer fixed point theorem. Covering spaces. van Kampens theorem. 2manifolds. Triangulations. Euler characteristic. Surgery, classification of compact 2manifolds. Three 50 minute lectures

Prerequisites: (21-355 or 21-235 or 21-455) and 21-373

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