| Friday, June 23 |
Motivation, logic, elementary set theory. |
Lecture 01 |
| Saturday, June 24 |
Cartesian products, power set, functions, cardinality. |
Lecture 02 |
| Monday, June 26 |
More cardinality, relations, quotient sets. |
Lecture 03 |
| Tuesday, June 27 |
The axiom of choice, product sets, well-ordering. |
Lecture 04 |
| Wednesday, June 28 |
Metric spaces, sequences, open and closed sets. |
Lecture 05 |
| Friday, June 30 |
Subspaces, continuity, and the metric topology. |
Lecture 06 |
| Monday, July 3 |
The metric topology, completeness, compactness. |
Lecture 07 |
| Tuesday, July 4 |
No class. |
|
| Wednesday, July 5 |
Theorems on compactness. |
Lecture 08 |
| Friday, July 7 |
Equivalence of compactness. |
Lecture 09 |
| Monday, July 10 |
Topological spaces, the Hausdorff property. |
Lecture 10 |
| Tuesday, July 11 |
Subbases and bases. |
Lecture 11 |
| Wednesday, July 12 |
Closure, interior, boundary, convergence, continuity. |
Lecture 12 |
| Friday, July 14 |
First and second countable, separable. |
Lecture 13 |
| Monday, July 17 |
Homeomorphisms, open and closed maps, subspaces. |
Lecture 14 |
| Tuesday, July 18 |
Review, catching up on previous notes. |
|
| Wednesday, July 19 |
Quotient spaces. |
Lecture 15 |
| Friday, July 21 |
Arts and crafts. |
Animation |
| Monday, July 24 |
Product spaces, homotopy. |
Lecture 16 |
| Tuesday, July 25 |
Orderable spaces. |
Lecture 17 |
| Wednesday, July 26 |
Regular and normal spaces. |
Lecture 18 |
| Friday, July 28 |
Urysohn’s Lemma. |
Lecture 19 |
| Monday, July 31 |
Connected spaces. |
Lecture 20 |
| Tuesday, August 1 |
No class. |
|
| Wednesday, August 2 |
Locally connected spaces. |
Lecture 21 |
| Friday, August 4 |
Nothing new. |
|
| Monday, August 7 |
Topological compactness. |
Lecture 22 |
| Tuesday, August 8 |
More compactness ideas. |
Lecture 23 |
| Wednesday, August 9 |
Paracompact spaces. |
Lecture 24 |
| Friday, August 11 |
Partitions of Unity. |
Lecture 25 |
| Monday, August 14 |
Metrization Theorems. |
Lecture 26 |
| Tuesday, August 15 |
Tychonoff’s Theorem. |
Lecture 27 |
| Wednesday, August 16 |
Manifolds. |
Lecture 28 |
| Friday, August 18 |
Groups. |
Lecture 29 |
| Monday, August 21 |
Topological Groups. |
Lecture 30 |
