Teacher Evaluations
The Math Dept will collect the evaluations via an online form.
See http://www.casa.uh.edu/TeacherEvaluation .
There is one copy of "General topology" by John L. Kelley placed on reserve (see the shelves on the ground floor).
Please write the solutions on separate pages (i.e., do not hand in a note-book).
Some of the problems might have the answer or a hint in the textbook. If
you have to hand in such a problem, you are welcome to use the hint but
have to still write a complete solution.
More difficult problems are marked by a *.
Problems that we should discuss are marked with ^. Problems marked with + are ones that you should also clarify.
NOTE: you have to prove all statements that are not proven in the textbook, unless they were discussed in class, or are part of the previous homework assignments.
| HOMEWORKS | |||
|---|---|---|---|
| HW # | Section | HAND IN | Solve only, do not hand in |
| 1. due Sep. 6 |
problem from Rudin | ||
| 2 | 2, mainly parts b,c,d,g,h | ||
| 3 | 4 | 1, 2, 6, 13, 14 | |
| 9 | 5 | ||
| 11 | 4, 5, 8 (we did not prove (b) in class; use either (MP) or (Z) to prove it) | ||
| 12 | Determine the convergent sequences for the finite complement topology on R (example 3 on page 77). Note: the limit need not be unique! | ||
| 2. due Sep. 20 |
Read sections 18, 20, 21, without the proofs. | ||
| 13 | 1 | 4, 5, 8^ | |
| 16 | 4 | 1+ | |
| 17 | 13 | 6, 11, 12, 15, 16^, 19+ | |
| 18 | 7(a) [prove "if and only if", not only one
implication], 13 |
1, 3+, 5, 7(b)^ | |
| 19 | 6 (ignore the box top.) | 3+ (for the product top. only), 4+, 9, 10* | |
| 20 | 3, 11 | ||
| 3. due Oct. 4 |
21 | 7 | 2, 3, 8 |
| 29.5 | 7 (this is from the exercises about nets, page 187) | ||
| 22 | 3 | 2^, 4^, 5 | |
| 23 | 7, 11 | 2, 3+, 4+, 5+, 10 | |
| 4. due Oct. 11 | 24 | 10 (see also 4 at Sec. 25) | 1^, 2^ [Hint: look at g(x):=f(x)-f(-x)], 3^, 8^, 11^ |
| 25 | 2(a) | 1+, 2(b), 4, 5 for 2(b) could look at example 6 in Sec. 23 |
|
| 26 | 5 | 1^, 2+, 8 [Hint: try with nets], 10 [Hint: look at the sets Kn:={f - fn ≥a}. I know this as Dini's Thm.] |
|
| 5. due Oct. 18 | 27 | 2 (b, d, e), 3 |
2 (a), 4, 5, 6 |
| 6. due Nov. 8 | 28 | 3 (a) and (b) only | 2, 6, 7 a^ (for a see "The Contraction Mapping Principle", prob. 5 in Sec. 43) and the rest of 7 |
| 7. due Nov. 20 or 27 | 29 | 8 | 5+, 1+, 2a (and b, once we know Tychonoff), 3?, 6+ |
| 37 | 1, 5* | ||
| 30 | 10 | 2+, 4^, 5, 9^ [will give a counterexample in class], 13+ | |
| 31 | 1+, 2+, 5, 6^ | ||
| 32 | 3, 1^, 2 (also true for T3 1/2), 4 | ||
| 33 | 7 | 2, 3, 4^ (see #1 in Sec. 30 for G-delta),
8^ (by 7, the conclusion holds for locally compact Hausdorff spaces; hint) |
|
| 35 | 1, 3^ (hint) | ||
| 34 | 3 | 4^, 5^, 9 | |
| 38 | 2+, 3, 4^, 6, 8, 9^, 10+ [will talk more about this section] | ||
| Ascoli-Arzela, etc. | 43 | 2+, 4 (see Lemma 48.3), 5^; 9 & 10 | |
| 45 | 2 (c)+, 3, 4, 7 | ||
| 46 | 2, 3, 4, 5 | ||
| 47 | 2, 5+ | ||
| Baire | 48 | 1, 2, 3, 7, 10 | |
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