| Problem Set |
Chapter |
Problems |
|---|---|---|
| 13 | 4 | Read Sections 4.1-4.19 |
| ∗22 | Prove the “if” part (the part not proved in class) of Theorem S.28. | |
| ∗23 | Suppose that f is a continuous, one-to-one correspondence from the compact metric space X to the metric space Y (that is, domain(f ) = X, range(f ) = Y). Show that f -1 is a function, and that it also is continuous. (In this case, f and f -1 are called homeomorphisms and the spaces X and Y are said to be homeomorphic.) | |
| n | manditory problem |
| ∗n | manditory problem, not from text |
| (n) | helper problem |
| [n] | ungraded problem |
| [∗n] | ungraded problem, not from text |
| {n} | optional problem |