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 Munkres, A first course in Topology.
Schedule
| Date | Class Topic | Remark |
|---|---|---|
| Aug 25 (Mon) | Sets, functions, relations | |
| Aug 27 (Wed) | Posets | |
| Aug 29 (Fri) | Axiom of Choice (intro) | Week 1 notes |
| Sep 1 (Mon) | No class (Labor Day) | Holiday |
| Sep 3 (Wed) | Cardinality I | |
| Sep 5 (Fri) | Cardinality II | Week 2 notes |
| Sep 8 (Mon) | Cardinality III | |
| Sep 10 (Wed) | Metric spaces | HW1 due |
| Sep 12 (Fri) | Ultrametric spaces | Week 3 notes |
| Sep 15 (Mon) | Open sets; topologies | |
| Sep 17 (Wed) | Bases for a topology | |
| Sep 19 (Fri) | Kuratowski closure axioms | Week 4 notes |
| Sep 22 (Mon) | Product topology on X×Y | |
| Sep 24 (Wed) | Subspace topology | HW2 due |
| Sep 26 (Fri) | Continuous functions | Week 5 notes |
| Sep 29 (Mon) | Continuous functions; homeomorphisms | |
| Oct 1 (Wed) | Product topology | |
| Oct 3 (Fri) | Quotient topology | Week 6 notes |
| Oct 6 (Mon) | Quotient topology | |
| Oct 8 (Wed) | Homotopy (introduction) | HW3 due |
| Oct 10 (Fri) | Homotopy (continued) | Week 7 notes |
| Oct 13 (Mon) | Review | |
| Oct 15 (Wed) | In-class Midterm Exam | Midterm |
| Oct 17 (Fri) | Homotopy (continued) | Week 8 notes |
| Oct 20 (Mon) | Sequences | |
| Oct 22 (Wed) | Nets | |
| Oct 24 (Fri) | Countability axioms | Week 9 notes |
| Oct 27 (Mon) | Separation axioms; normal spaces | |
| Oct 29 (Wed) | Normal spaces | HW4 due |
| Oct 31 (Fri) | Urysohn lemma | Week 10 notes |
| Nov 3 (Mon) | Urysohn metrization theorem | |
| Nov 5 (Wed) | Compact spaces | |
| Nov 7 (Fri) | Compact metric spaces | HW5 due; Week 11 notes |
| Nov 10 (Mon) | Compact metric spaces; completeness | |
| Nov 12 (Wed) | Sequential compactness | |
| Nov 14 (Fri) | Nets & compactness characterizations | Week 12 notes |
| Nov 17 (Mon) | Local compactness | |
| Nov 19 (Wed) | Paracompactness; partitions of unity | |
| Nov 21 (Fri) | Paracompactness; partitions of unity | HW6 due; Week 13 notes |
| Nov 24 (Mon) | No class (Thanksgiving recess) | |
| Nov 26 (Wed) | No class (Thanksgiving recess) | |
| Nov 28 (Fri) | No class (Thanksgiving recess) | |
| Dec 1 (Mon) | Connected spaces | |
| Dec 3 (Wed) | Path & local connectedness | |
| Dec 5 (Fri) | Totally disconnected spaces; Cantor set | Week 15 notes |
| Dec 8 (Mon) | Review | |
| Dec 10 (Wed) | Review | HW7 due |
| Dec 12 (Fri) | Reading Day (no class) | |
Final Exam: Monday, December 15, 7:30 a.m.–9:30 a.m.