Topological spaces, connectedness, compactness, continuous functions, separation axioms, function spaces. Metrization theorems, the Tychonoff theorem.
Students present and discuss the subject matter with faculty guidance.
Topics include the fundamental group and covering spaces. Open to all students who have had 18.906 or the equivalent, not only prospective topologists. Introduces new and significant developments in algebraic topology with the focus on homotopy theory and related areas. An introduction to differential geometry, with emphasis on curves and surfaces. Frenet formulas, fundamental forms, curvature, Gauss' theorem, geodesics, Riemannian manifolds.