Problem Set
|
Chapter
|
Problems
|
| 02 |
∗4 |
Finish proving Theorem M.7. Note: I expect you to use the definitions of limit point and open that I gave in class, not the ones in Rudin, Section 2.18.
|
|
∗5 |
Let (X, d ) be a metric space with subset E. Prove that E ′ is closed. |
|
∗6 |
Suppose that (xn ) is a sequence in a metric space (X, d ). Show that (xn ) converges if and only if every subsequence of (xn ) converges to the same limit. (See me if the idea of a subsequence is a new one.)
|
|
2 |
6, 7 -- You need not re-prove the first claim of 6.
|