May 8: Existence of covering spaces.
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