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Graduate Courses

General Topology

Fall: 12 units

  • Finite and infinite sets, Axiom of Choice, Zorn lemma
  • Topological Spaces (basics of open/closed sets, bases, countability, product spaces, quotient spaces)
  • Continuity
  • Connectedness, Compactness, Tychonoff Theorem (time permitting: Stone-Cech compactification)
  • Separation Axioms, Urysohn Lemma and Tietze Extension Theorems, Urysohn Metrization Theorem)
  • Metric Spaces (Cauchy sequences, completeness, Baire Category Theorem, completion, separability, sequential compactness, total boundedness, compactness, Arzela-Ascoli Theorem, partition of unity)
  • Brouwer's Fixed Point Theorem