Math 530, Fall 2006: Homework
Please turn in no more than five (5) proofs a week.
Feel free to ask me for solutions!
| Problems | Comments | Hints/Solutions | ||
|---|---|---|---|---|
| p. 83 #1–8 | ||||
| pp. 91–92 #1–7, 10 | ||||
| Do every other one of these, more if you have time: pp. 100–102 #1–14, 16–21 | #20 refers to #19. #21 is a challenge problem. |
Solution to #21 (It's a little hard to read, but the proof is on pages 1 and 2. The rest of the paper starts going into more depth.) | ||
| pp. 111–112 #1, 2, 4, 5, 8, 10, 11, 13 | ||||
| Turn in a first draft of two (2) problems from the midterm by Tues., Oct. 31. §2-19 #1–4, 6–8, 10 CHALLENGE: #9 |
Focus on the product topology | |||
| §2-20 #1a, 2, 3, 4, 7d |
Turn in a first draft of one of these by Tues., Nov. 7. | |||
| §3-23 #2, 3, 5, 9, 12 CHALLENGE: Is R^2 in the Zariski topology connected? |
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| §3-24 #1, 2, 10 Also, pick two letters of the alphabet which are not homeomorphic, and prove that they are not. |
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| §3-26 #2, 3, 6, 8, 12 | ||||
| §3-27 #1, 2, 4, 6 | ||||
| §3-29 #1, 6, 8 | Def. of locally compact and one-point compactification only | |||
| §4-30 #1, 6, 8 | Def. of second countable, Thm. 30-3 only | |||
| §4-31 #1, 2, 3, 6 | ||||
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