Last updated Wed Dec 7 15:30 EST 2016
Due-date (unenforced): Friday, 12/9/16
There are no hand-in problems, and classes end on Wednesday 12/7/15. But try to do each the problem as soon as possible after we've covered the relevant material in class, and try to do them all by the date above, so that you have time to ask me questions and digest my answers.
- A: Rosenlicht pp. 90–95/ 1bc, 3, 4, 6–8, 9c, 10, 14–18, 21, 29a.
Notes: (1) "Discuss the continuity of ..." means: Determine, with proof, at which points the indicated function is/isn't continuous. (2) Problem #7 can be done from scratch, but can be done more efficiently by using the result of #3 (once you've done #3). (3) 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. (4) If you do not find #21 harder than the other problems above, you are probably doing something wrong.
- B: Click here for non-book problems.
- C: Read the handout Continuity, Images, and Inverse Images (also available on the Miscellaneous handouts page).
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