|
| | 1a | | * |
| Due 26 August |
|
Please show that the rationals are countably infinite,
i.e., count them. |
| | 1b | | p. 12 |
| Due 31 August |
| # 1b, 3a,b, 4b,d |
| | 2 | | pp. 12-13 |
| Due 7 September |
| # 7a,c,f, 8, 9 |
| | 3 | | pp. 29-30 |
| Due 9 September |
| # 1, 2a, 3, 5a,b,c |
| | 4 | | pp. 30-31 |
| Due 15 September |
| # 7, 9, 10, 13, 14 (find only a rational x)
|
| | 5 | | p. 61 |
| Due 22 September |
| # 1a,b, 3, 4, 6 |
| | | | * |
| | | A. Prove that the intersection
of a finite number of open set Gi is open. |
| | 6 | | * |
| Due 26 September | | B. Give an example
where the countably infinite
union of closed sets is not closed. |
| | | | p. 61 |
| |
| # 5, 7, 8 |
| | 7 | | p. 62 |
| Due 29 September |
| # 9, 12, 13, 14 |
| | 8 | | p. 62 |
| Due 4 October |
| # 15, 16a,c, 17b,c |
| | 9 | | * |
| |
| A. Prove the in-class version of Corollary 1, p. 56: |
| | | | * |
| Due 7 |
| Any bounded sequence in Rn has a convergent
subsequence. |
| | | | * |
| October |
| B. Please give an example to show why the nesting property fails |
| | | | * |
| |
| for a sequence of nonempty, closed, but unbounded sets in Rn . |
| | | | p. 64 |
| |
| # 27, 29 |
| | 10 | | p. 64 |
| Due 11 |
| # 28 |
| | | | pp. 90-92 |
| October |
| # 1b,d, 9a, 10a,b, 14a |
|
