Difference between revisions of "10-327/Homework Assignment 1"

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* Dror do you mean question 3 and 4 on page 100? There is no question 3 and 4 on page 101. -Kai
 
* Dror do you mean question 3 and 4 on page 100? There is no question 3 and 4 on page 101. -Kai
* Sorry and thanks for the correction, indeed I meant page 100. (BTW, next time you sign a wiki submission, use "<nowiki>~~~~</nowiki>" (four "tilde" symbols) and see what it does). [[User:Drorbn|Drorbn]] 18:03, 26 September 2010 (EDT)
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** Sorry and thanks for the correction, indeed I meant page 100. (BTW, next time you sign a wiki submission, use "<nowiki>~~~~</nowiki>" (four "tilde" symbols) and see what it does). [[User:Drorbn|Drorbn]] 18:03, 26 September 2010 (EDT)

Revision as of 18:04, 26 September 2010

Read sections 12 through 17 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 18 through 22, just to get a feel for the future.

Solve and submit the following problems. In Munkres' book, problems 4 and 8 on pages 83-84, problems 4 and 8 on page 92, problems 3 and 4 on page 100, and, for extra credit, the following problem:

Problem. Let X and Y be topological spaces and let A\subset X and B\subset Y be subsets thereof. Using only the definitions in terms of continuity of certain functions, show that the topology induced on A\times B as a subset of the product X\times Y is equal to the topology induced on it as a product of subsets of X and of Y. You are allowed to use the fact that two topologies {\mathcal T}_1 and {\mathcal T}_2 on some set W are equal if and only if the identity map regarded as a map from (W, {\mathcal T}_1) to (W, {\mathcal T}_2) is a homeomorphism. Words like "open sets" and "basis for a topology" are not allowed in your proof.

Due date. This assignment is due at the end of class on Thursday, September 30, 2010.

Dror's notes above / Student's notes below
  • Dror do you mean question 3 and 4 on page 100? There is no question 3 and 4 on page 101. -Kai
    • Sorry and thanks for the correction, indeed I meant page 100. (BTW, next time you sign a wiki submission, use "~~~~" (four "tilde" symbols) and see what it does). Drorbn 18:03, 26 September 2010 (EDT)