21-651
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