| Friday, June 24 |
Motivation, logic, elementary set theory. |
Lecture 01 |
| Saturday, June 25 |
Cartesian products, power set, functions, cardinality. |
Lecture 02 |
| Monday, June 27 |
More cardinality, relations, quotient sets. |
Lecture 03 |
| Wednesday, June 29 |
The axiom of choice, product sets, well-ordering. |
Lecture 04 |
| Thursday, June 30 |
Metric spaces, sequences, open and closed sets. |
Lecture 05 |
| Friday, July 1 |
Subspaces, continuity, and the metric topology. |
Lecture 06 |
| Monday, July 4 |
No class. |
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| Wednesday, July 6 |
Catching up and review. |
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| Thursday, July 7 |
The metric topology, completeness, compactness. |
Lecture 07 |
| Friday, July 8 |
Heine-Borel and Bolzano-Weierstrass Theorems. |
Lecture 08 |
| Monday, July 11 |
Equivalence of compactness. |
Lecture 09 |
| Wednesday, July 13 |
Topological spaces, Hausdorff, generated topology. |
Lecture 10 |
| Thursday, July 14 |
Subbases and bases. |
Lecture 11 |
| Friday, July 15 |
Closure, interior, boundary, convergence, continuity. |
Lecture 12 |
| Monday, July 18 |
First and second countable, separable. |
Lecture 13 |
| Wednesday, July 20 |
Homeomorphisms, open and closed maps, subspaces. |
Lecture 14 |
| Thursday, July 21 |
Quotient spaces. |
Lecture 15 |
| Friday, July 22 |
Arts and crafts. |
Animation |
| Monday, July 25 |
Product spaces, the box topology. |
Lecture 16 |
| Wednesday, July 27 |
The order topology, orderable spaces. |
Lecture 17 |
| Thursday, July 28 |
Regular and normal spaces. |
Lecture 18 |
| Friday, July 29 |
Urysohn’s Lemma, Urysohn’s metrization theorem. |
Lecture 19 |
| Monday, August 1 |
Connectedness, path-connectedness. |
Lecture 20 |
| Wednesday, August 3 |
Locally connected, locally path-connected. |
Lecture 21 |
| Thursday, August 4 |
Compactness, sequential compactness. |
Lecture 22 |
| Friday, August 5 |
Countably compact, limit point compact, Lindelof. |
Lecture 23 |
| Monday, August 8 |
Locally compact, paracompact, Stone’s theorem. |
Lecture 24 |
| Wednesday, August 10 |
Partitions of unity. |
Lecture 25 |
| Thursday, August 11 |
Metrization theorems. |
Lecture 26 |
| Friday, August 12 |
Alexander’s subbasis theorem, Tychonoff’s theorem. |
Lecture 27 |
| Monday, August 15 |
Compactifications, completely metrizable spaces. |
Lecture 28 |
| Wednesday, August 17 |
Locally Euclidean spaces. |
Lecture 29 |
| Thursday, August 18 |
Manifolds. |
Lecture 30 |
| Friday, August 19 |
The topology of manifolds. |
Lecture 31 |
| Monday, August 22 |
Covering spaces, the hyperbolic plane. |
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| Wednesday, August 24 |
Classification of surfaces. |
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| Thursday, August 25 |
(Optional) Review for final. |
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