| Date | Section | Problems | Remarks | Due |
|---|---|---|---|---|
| 2/11 | 1-7 | Scan these sections. | F 2/15 | |
| 2/13 | 1 | 2 | Omit explanations. | M 2/18 |
| 2/15 | 3 7 | 15 5 | Dictionary order Omit explanations. | M 2/25 |
| 2/18 | 8 | 7 | Extra credit | M 2/25 |
| 2/18 | 9 | Entertainment: Problem 6 | ||
| 2/18 | 10 | 1, 3 | Well-ordering problems | M 2/25 |
| 2/20 | 20 | 9, 10 | Euclidean & "l2" metrics | M 2/25 |
| 2/22 | 20 |
lim ||x||p = square norm
Three problems | Extra credit Required problems | M 3/4 |
| 2/25 | Prove the Borel-Lebesgue theorem. | JM, KP, ET & EP | W 2/27 | |
| 3/1 | 12, 13 | 2, 4 | Topologies & bases | M 3/11 |
| 3/4 | 14 15 16 | 4, 6, 10 | Order topology Product topology Subspace topology | M 3/11 |
| 3/6 | 17 | 6, 7, 8 | Closed sets and limit points | M 3/11 |
| 3/8 | 17 18 | 12 1 | Hausdorff spaces Continuous functions | W 3/13 |
| 3/18 | 20 20 21 | 3: continuity of distance
8: topologies on omega-tuples 7: uniform continuity topology | 3: AG & KP 8: JM, EP, ET 7: volunteer | F 3/22 |
| 3/18 3/22 | 20 21 | 3, 8 7 | Hints
Exercise 20.3 (ps) Exercise 20.8 (ps) | W 3/27 |
| 3/25 | 23 | (2 or 5) and 10 | Connectedness | F 4/12 |
| 3/27 | 24 | 3 5 | Cf. MCS 331 Exam 2b
Cf. old HW, Exam 1b | F 4/12 |
| 3/27 | 24 | |||
| 4/8 | 25
26 | 1
4 | S&S p. 32
| F 4/12
M 4/15 |
| 4/10 | 26 | |||
| 4/12 | 26, 28
+S&S | 27.6: Cantor set
(recommended) | ||
| 4/15 | 27 | Student presentations | Use transparencies. | M 4/15 |
| 4/17 | 28, 29 | Look at #29.6 . | ||
| 4/19 | 20-29 | In-class exam
Take-home problems | Closed book
Open book | F 4/19
M 4/22 |
| 4/22 | 30 | 1, 5 | M 4/29 | |
| 4/24 | 31 | handouts | spreadsheets | M 4/29 |
| 4/26 | 30-31 | Presentations | Grid: Space by Hereditary? Products? | |
| 4/29 | 32 | 1 | Normality is weakly hereditary. | M 5/6 |
| 5/1 | 33 | 3
1 | Urysohn's lemma is easy in metric space.
33.1: Extra credit | M 5/6 |
| 5/3 | 34,35,40,11 | 35.1 | Whirlwind tour: See Thms 34.1, 35.1, 40.3, Ex. 11.8. | M 5/13 |
| 5/6 | 37 | 1
A Tychonoff problem (ps) (pdf) (html) | Draw epsilon-ball centered at 0 in D-metric if epsilon=1/4 for Fri. | M 5/13 |
| 5/8 | 43 | 5
9 | #43.5 Hint
1
2
3
4
#43.9 Hint (a) | W 5/15 |
| 5/10 | 43-44 | AG presentation | ||
| 5/13 | 43 | #43.5, #43.9 | Student presentations | |
| 5/15 | 45 | Extra credit: #45.3 | W 5/22 | |
| 5/17 | Sprecher 35-37 |