Math 564: Topology
Spring 2018

Office Hours (in MCS 237B): M 12:00-1:00, W 1:00-2:00 and 3:30-4:00, F 1:30-2:30

COURSE SYLLABUS

All grades are recorded on Blackboard. Check it regularly to be sure assignments are entered correctly.

Problem Sets

• Problem Set 1 (solutions)
• Problem Set 2 (solutions)
• Problem Set 3 (solutions)
• Problem Set 4 (solutions)
• Problem Set 5 (solutions)
• Problem Set 6 (solutions)
• Problem Set 7 (solutions)
• Problem Set 8 (solutions)
• Problem Set 9 (solutions)

Lecture Notes

Disclaimer: The notes summarize lecture but don't always have full explanations/answers (partly on purpose... come to class). Ask me if something isn't clear or you find a typo.

• Jan 19 - Introduction
• Jan 22 - Bases and Comparing Topologies
• Jan 24 - Order Topology and Comparing Topologies
• Jan 26 - Product Topology
• Jan 29 - Subspace Topology
• Jan 31 - Closed Sets, Limit Points, etc
• Feb 2 - Continuity
• Feb 5 - Continuity II
• Feb 7 - Product vs Box Topology
• Feb 9 - Metric Topology
• Feb 12 - Metric Topology II
• Feb 14 - Uniform Convergence
• Feb 20 - Quotient Topology
• Feb 21 - Connected Sets
• Feb 23 - Connected and Path Connected Sets
• Feb 26 - Connected Sets/Components Practice
• Feb 28 - Compact Sets
• March 2 - Compact Sets II
• March 12 - Compact Sets III
• March 14 - Cantor Set and Limit Point Compactness
• March 16 - Sequential Compactness and Contraction Maps
• March 19 - Practice
• March 21 - Compactifications
• March 23 - Completeness
• March 26 - Completeness II and Space-Filling Curves
• March 28 - Completions
• April 2 - Separation Axioms
• April 4 - Urysohn's Lemma
• April 9 - Urysohn's Metrization Theorem
• April 11 - Path Homotopy
• April 13 - Fundamental Group
• April 18 - Fundamental Group II
• April 20 - Fundamental Group III
• April 23 - Covering Spaces
• April 25 - Borsuk-Ulam Theorem
• April 27 - Homotopy Equivalence