| Problem Set |
Chapter |
Problems |
|---|---|---|
| 05 | ∗10 | Let E be a subset of a metric space X. Show that E is dense in X if and only if for each point a in X and each r > 0, the ball B(a, r) has nonempty intersection with E. |
| ∗11 | In my copy of Rudin's text, Theorem 2.38 says, “If {In} is a sequence of intervals from the real line such that In ⊃ In+1 (n = 1, 2, 3, ...), then ∩n In is nonempty.” Show that this statement is, in fact, false. | |
| ∗12 | Prove the Nested Interval Theorem (M.17). | |
| n | manditory problem |
| ∗n | manditory problem, not from text |
| (n) | helper problem |
| [n] | ungraded problem |
| [∗n] | ungraded problem, not from text |
| {n} | optional problem |