Last updated Wed Dec 5 18:25 EST 2018
"Due date": Mon. 12/10/18 (the day of the final exam). There are no hand-in problems.
You should do all the reading, and at least attempt to do all of the problems below, before the final exam. (The reading should be done earlier, as indicated.) On the final exam you'll be responsible for the material in this assignment.
C: (Reading)
- Read Rosenlicht Section IV.3. Do this by Tuesday night, 12/4/18 (earlier if possible).
- Read the handout Continuity, Images, and Inverse Images (also available on the Miscellaneous handouts page).
A: Rosenlicht Chap. IV/ 6–8, 14, 16, 29a.
Notes: (1) Problem #7 can be done straight from definitions, but can be done more efficiently by using the result of #3. (2) In #16, to use Rosenlicht's hint you have to prove that both halves of the hint are true. Note that in general a continuous function \(f\) from one metric space to another need not carry closed sets to closed sets. (For an example, see the handout in part C of this assignment, Example 2a.) To use Rosenlicht's hint, part of what you have to figure out is why the \(f\) in this problem does carry closed sets to closed sets.
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