|
| | 1a | | * |
| Due 10 January |
| Please show that the rationals are countably infinite. |
| | 1b | | p. 12 |
| Due 14 January |
| # 1a,b, 2a,c, 3c, 4d |
| | 2 | | p. 12 |
| Due 17 January |
| # 7, 8, 9 |
| | 3 | | pp. 29-30 |
| Due 23 January |
| # 1, 3, 4b, 5a,c,d, 6 |
| | 4 | | pp. 30-31 |
| Due 27 January |
| # 7, 9, 10, 11, 13, 14 (find a rational x) |
| | 5a | | p. 61 |
| Due 30 January |
| # 1a,c |
| | 5b | | p. 61 |
| Due 4 February |
| # 2, 3, 4 |
| | | | * |
| Due 7 February | | A. Prove that the intersection
of a finite number of open set Gi is open. |
| | 6 | | * |
| Due 7 February | | B. Give an example
where the countably infinite
union of closed sets is not closed. |
| | | | p. 61 |
| Due 7 February |
| # 5, 7 |
| | 7 | | p. 62 |
| Due 12 February |
| # 9, 11, 12, 13 |
| | 8 | | p. 62 |
| Due 19 February |
| # 15, 16a, 17a,b |
| | | | * |
| |
| 1. Prove the in-class version of Corollary 1, p. 56: |
| | | | * |
| Due 20 |
| Any bounded sequence in Rm has a convergent
subsequence. |
| | 9 | | * |
| February |
| 2. Please give an example to show why the nesting property fails |
| | | | * |
| |
| for a sequence of nonempty, closed, but unbounded sets in Rm . |
| | | | p. 64 |
| |
| # 27, 30 |
| | 10 | | p. 64 |
| Due 25 |
| # 28 |
| | | | pp. 90-92 |
| February |
| # 1b, 9a, 10, 11, 14a |
|