The homework problems are to be found in the textbook; 'a.b' means 'Problem b in Paragraph a'.
It is strongly suggested that you treat all the problems listed here.
Policy: homework should be submitted no later than 5pm on the due date. Let your instructor know in advance if you feel that you need extra time.
wk | date | reading | topic | homework / comments | |
1 | 06/26 | Introduction | 1.1, 1.3, 1.9, 2.2, 2.4, 2.5 | ||
2 | 06/29 | §1 to §6 | Basic set theory: finite and infinite sets | 3.3, 3.9, 3.11, 4.1, 4.2, 4.9, 4.11 | |
06/30 (x) | §1 to §6 | Basic set theory: countable sets | 5.4, 6.5, 6.7 | ||
07/01 | No class | PC away | |||
07/03 | No class | College Holiday | |||
Homework #1, due Tuesday 07/07. | |||||
3 | 07/06 | Examples of metric spaces | |||
07/07 (x) | Metric spaces and continuous maps | Homework #2, due Monday 07/13 and solution. | |||
07/08 | §12, §13 | Topological spaces: topologies and bases | |||
07/10 | §13 | Topological spaces: bases | 13.1, 13.3, 13.4, 13.5, 13.6, 13.8 | ||
4 | 07/13 | §14 | The order topology | ||
07/14 (x) | §15 | The product topology on X × Y | 16.2, 16.3, 16.6, 16.9 | ||
07/15 | §16 | The subspace topology | Homework #3, due Monday 07/20 and solution. | ||
07/17 | §17 | Closed sets | |||
5 | 07/20 | §17 | Closure, accumulation points | 17.3, 17.5, 17.6, 17.7, 17.8 | |
07/21 (x) | §17 | Hausdorff and T_{1} spaces | 17.12, 17.14, 17.15, 17.16 | ||
07/22 | Midterm 1 (solution) | ||||
07/24 | Guest lecture | The problem with Topology, by James Binkoski (after T. Maudlin) | Homework #4, due Wednesday 07/29 and solution. | ||
6 | 07/27 | §18 | Continuous maps | 18.2, 18.3, 18.5, 18.8 | |
07/28 (x) | §18 | Continuous maps | Guest lecture by D. Freund | ||
07/29 | Not in text | Homeomorphisms and the category Top | An introduction to categories can be found in course notes by P. Schapira. | ||
07/31 | §19 | Products of topological spaces | 19.1, 19.2, 19.3, 19.4, 19.7, 19.8, 19.10 | ||
Homework #5, due Friday 08/07 and solution. | |||||
7 | 08/03 | §20 | The metric topology | 20.1, 20.3, 20.4, 20.5, 20.6 | |
08/04 (x) | §20 | The metric topology | 21.3, 21.6, 21.7, 21.8 | ||
08/05 | §21 | Sequences in metric spaces - Functors | Homework #6, due Monday 08/10 and solution. | ||
08/07 | §23 | Connected spaces | Guest lecture by D. Freund | ||
8 | 08/10 | §24, §25 | Path connectedness, connected components | 23.4, 23.5, 23.7, 24.1, 24.2, 24.3 | |
08/11 (x) | §26 | Compact spaces | |||
08/12 | Midterm 2: in-class (solution), take-home (solution) | ||||
08/14 | §26 | Compact spaces | 26.1, 26.2, 26.3, 26.5, 26.7, 26.8 | ||
9 | 08/17 | §27 | Compact subspaces of the real line | ||
08/18 (x) | §28 | Limit point and sequential compactness | 28.2, 28.6, 28.7 | ||
08/19 | §29 | Local compactness | Homework #7, due Tuesday 08/25 and solution. | ||
08/21 | §31 - §34 | Separation properties and metrizability | |||
10 | 08/24 | Not in text | Topological properties of matrix groups | ||
08/25 (x) | No class | ||||
08/26 | Not in text | Topological properties of matrix groups | |||
08/29 | Final examination and solution. |