| Date | Topic | Book | HomeworkHmwk | Practice ProblemsProbs | |
|---|---|---|---|---|---|
| Sept. | 3 | Introduction to the course I | §3.1 | ||
| 5 | Introduction II | ||||
| 6 | Introduction III | §3.3 | |||
| 10 | Homeomorphisms | ||||
| 12 | The subspace topology | §3.5 | |||
| 13 | Subspaces II | §3.5 | H1 | ||
| 17 | Generators and bases for topologies | §3.1 | A1 | ||
| 19 | Generators and bases II | §3.1 | |||
| 20 | Introduction to Categories | §10.4 | H2 | ||
| 24 | Definitions by diagrams; functors | §10.4 | A2 | ||
| 26 | Definitions via universal properties | §10.4 | |||
| 27 | Products and the product topology | §3.6 | H3 | ||
| Oct. | 2 | Officially a Monday (no class) | A3 | ||
| 3 | Products II | §3.6 | |||
| 4 | Quotient spaces | §5.1 | H4 | ||
| 8 | Quotient spaces II | §5.2 | A4 | ||
| 10 | Examples of quotient spaces | ||||
| 11 | More quotient examples | H5 | |||
| 15 | |||||
| 17 | Fall Break | ||||
| 18 | |||||
| 22 | Separation properties | §7.6 | A5 | ||
| 24 | Connectedness of topological spaces I | §4.1 | |||
| 25 | Connectedness II | §4.1 | H6 | ||
| 29 | Compact and quasi-compact spaces | §4.4 | A6 | ||
| 31 | Compact subsets of $\mathbb{R}^n$ | §4.4 | |||
| Nov. | 1 | Tychonoff's theorem I | §7.2 | H7 | |
| 5 | Tychonoff's theorem II | §8.4 | A7 | ||
| 7 | Separation conditions II | §7.6 | |||
| 8 | Metric spaces | §3.4 | H8 | ||
| 12 | Topology as a language | A8 | |||
| 14 | Introduction to the fundamental group | §11.1 | |||
| 15 | Introduction to $\pi_1$ II | §11.2 | H9 | ||
| 19 | Introduction to $\pi_1$ III | §11.3 | A9 | ||
| 21 | $\pi_1(S^n)$, $n\geq 2$ | §11.4 | |||
| 22 | $\pi_1(S^1)$, I | H10 | |||
| 26 | $\pi_1(S^1)$ II and covering spaces | §12.2 | A10 | ||
| 28 | $\pi_1(S^1)$ III + first applications | §12.4 | |||
| 29 | More applications of $\pi_1(S^1)$ | §12.5 | H11 | ||
| Dec. | 3 | Still more applications of $\pi_1(S^1)$ | §12.5 | A11 | |
| 5 | |||||
| 6 | H12 | ||||
| 10 | A12 |