Course Objectives
This graduate-level course introduces point-set topology. Topics include topological spaces, continuity, compactness, connectedness, countability and separation axioms, and an introduction to homotopy, etc.
See the course syllabus (PDF) here.
Textbook & References
Stephen Willard, General Topology.
James R. Munkres, Topology, 2nd edition.
Schedule
Tentative topics; meetings are Monday/Wednesday/Friday, 12:00–12:50 p.m., in MSB 312. Dates follow the Mizzou Fall 2026 academic calendar. Veterans Day (November 11) has no classes. Fall Reading Day has been removed, so December 11 is a regular class day and the final day of classwork.
| Date | Class Topic | Remark |
|---|---|---|
| Aug 24 (Mon) | Sets, functions, relations | Classwork begins |
| Aug 26 (Wed) | Posets | |
| Aug 28 (Fri) | Posets | Week 1 notes |
| Aug 31 (Mon) | Axiom of Choice | |
| Sep 2 (Wed) | Cardinality I | |
| Sep 4 (Fri) | Cardinality II | Week 2 notes |
| Sep 7 (Mon) | No class | Labor Day |
| Sep 9 (Wed) | Metric spaces | |
| Sep 11 (Fri) | Ultrametric spaces | Week 3 notes |
| Sep 14 (Mon) | Open sets; topologies | HW1 due |
| Sep 16 (Wed) | Bases for a topology | |
| Sep 18 (Fri) | Kuratowski closure axioms | Week 4 notes |
| Sep 21 (Mon) | Product topology on X×Y | |
| Sep 23 (Wed) | Midterm 1 review | |
| Sep 25 (Fri) | Midterm Exam 1 | 12:00–12:50 p.m. |
| Sep 28 (Mon) | Subspace topology | |
| Sep 30 (Wed) | Continuous functions | HW2 due |
| Oct 2 (Fri) | Continuous functions; homeomorphisms | Week 5 notes |
| Oct 5 (Mon) | Product topology | |
| Oct 7 (Wed) | Quotient topology | |
| Oct 9 (Fri) | Quotient topology | Week 6 notes |
| Oct 12 (Mon) | Homotopy (introduction) | |
| Oct 14 (Wed) | Homotopy (continued) | HW3 due |
| Oct 16 (Fri) | Sequences | Week 7 notes |
| Oct 19 (Mon) | Nets | |
| Oct 21 (Wed) | Countability axioms | |
| Oct 23 (Fri) | Separation axioms | Week 8 notes |
| Oct 26 (Mon) | Normal spaces | |
| Oct 28 (Wed) | Urysohn lemma | |
| Oct 30 (Fri) | Midterm 2 review | |
| Nov 2 (Mon) | Midterm Exam 2 | 12:00–12:50 p.m. |
| Nov 4 (Wed) | Urysohn metrization theorem | |
| Nov 6 (Fri) | Compact spaces | HW4 due |
| Nov 9 (Mon) | Compact metric spaces | |
| Nov 11 (Wed) | No class | Veterans Day |
| Nov 13 (Fri) | Compact metric spaces; completeness | |
| Nov 16 (Mon) | Sequential compactness | |
| Nov 18 (Wed) | Nets & compactness characterizations | |
| Nov 20 (Fri) | Local compactness | HW5 due |
| Nov 23 (Mon) | No class | Thanksgiving recess |
| Nov 25 (Wed) | No class | Thanksgiving recess |
| Nov 27 (Fri) | No class | Thanksgiving recess |
| Nov 30 (Mon) | Paracompactness; partitions of unity | Classwork resumes |
| Dec 2 (Wed) | Paracompactness; partitions of unity | |
| Dec 4 (Fri) | Connected spaces | HW6 due |
| Dec 7 (Mon) | Path & local connectedness | |
| Dec 9 (Wed) | Totally disconnected spaces; Cantor set | |
| Dec 11 (Fri) | Review and course wrap-up | Classwork ends; regular class day |
Final Examination: Monday, December 14, 12:30–2:30 p.m.