| Lec. | Date | Section | Topic |
|---|---|---|---|
| 1/18 | Martin Luther King Day - no classes | ||
| 1 | 1/20 | 1, 5 | Introduction. Metric spaces. Metrics on R and Rn. |
| 2 | 1/22 | 5 | Metric spaces: more examples. |
| 3 | 1/25 | 5 | Product spaces. Continuous functions on R and on metric spaces. |
| 4 | 1/27 | 5 | Continuous functions from a metric space to R. |
| 5 | 1/29 | 5 | Continuous functions on metric spaces. |
| 6 | 2/1 | 5 | Bounded sets. Open balls in metric spaces. |
| 7 | 2/3 | 5 | Open sets in metric spaces. |
| 8 | 2/5 | 5, 6 | Continuity in terms of open sets. Closed sets. |
| 9 | 2/8 | 6 | The closure of a set. |
| 10 | 2/10 | 6 | The interior and the boundary of a set. |
| 11 | 2/12 | 6 | Convergence in metric spaces. |
| 12 | 2/15 | 6 | Equivalent metrics. |
| 13 | 2/17 | 6, 7 | Homeomorphisms and isometries. Topological spaces: motivation. |
| 14 | 2/19 | 7 | Topological spaces: definition and examples. |
| 15 | 2/22 | Review. | |
| 16 | 2/24 | Exam 1 covering Chapters 5 and 6. | |
| 17 | 2/26 | 8 | Continuous maps of topological spaces. |
| 18 | 3/1 | 8, 9 | Bases of topology. Closed sets in topological spaces. |
| 19 | 3/3 | 9 | The closure of a set and dense sets in a topological space. |
| 20 | 3/5 | 9 | The interior and the boundary of a set in a topological space. |
| 21 | 3/8 | 10 | Subspaces of topological spaces. |
| 22 | 3/10 | 10 | Products of topological spaces. |
| 23 | 3/12 | 10 | Topological products and continuity. |
| 24 | 3/15 | 11+ | Separation axioms. |
| 25 | 3/17 | 11+, 12 | Separation axioms. Connected spaces. |
| 26 | 3/19 | 12 | Connectedness. |
| 27 | 3/22 | 12 | Connectedness and path-connectedness. |
| 28 | 3/24 | 12, 13 | Path-connectedness. Compactness: motivation and definition. |
| 29 | 3/26 | 13 | Compact and noncompact sets. |
| 30 | 3/29 | Review. | |
| 31 | 3/31 | Exam 2 covering Chapters 7-12. | |
| 32 | 4/2 | 13 | Properties of compact sets. |
| 33 | 4/5 | 13 | Compactness of the product. Continuous maps on compact spaces. |
| 4/7 | Wellness day - no classes | ||
| 34 | 4/9 | 14 | Sequential compactness in metric spaces. |
| 35 | 4/12 | 15 | Quotient spaces: introduction and definitions. |
| 36 | 4/14 | 15 | Quotient spaces and quotient maps. The circle. |
| 37 | 4/16 | 15 | The torus, Klein bottle, and real projective plane. |
| 38 | 4/19 | The fundamental group: definition. | |
| 39 | 4/21 | The fundamental group: discussion. Simply connected spaces. | |
| 40 | 4/23 | The fundamental group: sphere, circle, and real projective plane. | |
| 41 | 4/26 | More on the fundamental group. | |
| 42 | 4/28 | Review. | |
| 43 | 4/30 | Q & A | |