May 3: Fundamental groups of spheres, and uniqueness of universal covers.

May 1: Fundamental group of the circle.

April 26: Homotopy of paths and the fundamental group.

April 24: Arzela-Ascoli and application to shortest curves

April 19: Space-filling curve, compact metric spaces, function families

April 17: Complete metric spaces

April 12: Stone-Chech compactification and Tychonoff's Theorem

April 10: Embedding of manifolds

April 5: Urysohn metrization and Tietze extension

April 3: normal spaces and Urysohn lemma

March 29: countability and separation axioms

March 27: limit point compactness, local compactness, and compactifications.

March 22: compactness in R^n (partial recording).

March 6: compactness.

February 15: non-metrizability of some infinite spaces, uniform limit theorem, introduction to quotient spaces

February 13: metric spaces, interaction with product topology

February 8: homework problems by audio

February 8: continuity continued, product and box topologies

February 6: continuity

February 1: closed sets, closures, Hausdorff spaces

January 30: bases, product topology, subspace topology

January 25: bases, infinitude of primes, and order topology

January 23: syllabus, introductions, and definition of a topology