MAA 4211, Section 16G0 — Fall 2016
Assignment 7
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).
General homework page
Class home page