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Graduate Courses
21651
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: StoneCech 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, ArzelaAscoli Theorem, partition of unity)
 Brouwer's Fixed Point Theorem
