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