$ \def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}} \def\calT{{\mathcal T}} \def\Lim{{\operatorname{Lim}}} $

(25)

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Homework Assignment #5

Post. If you have an excellent solution set for a past assignment, I'll be happy to post it as explained at About.html under "Solution Sets".

Reread sections 23 and 24 in Munkres' textbook (Topology, 2nd edition), and then read sections 26 and 27 of the same. 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 29 and 37 through 38, just to get a feel for the future.

Solve following problems, though submit only the underlined ones. In Munkres' book, problems 1, 2, 3, 8a, 8bcd, and 10 on pages 157-159, and problems 1, 4, 5, 6, 7, 8, 9, and 12 on pages 170-172.

In addition, without using Tychonov's theorem (whose name I can't even spell), prove that the infinite product $\{0,1\}^\omega$ is compact, where each factor, the 2-element set $\{0,1\}$, is taken with the discrete topology. Do not submit your solution of this problem.

Due date. This assignment is due at the end of class on Thursday, November 1, 2018. New! If you can, please use the Homework Submission Cover Page to help with faster returns and to help with privacy.