\( \def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}} \def\calT{{\mathcal T}} \def\Lim{{\operatorname{Lim}}} \)
© | Dror Bar-Natan: Classes: 2018-19: MAT327F - Introduction to Topology: (33) Next: Map of Chapter 4
Previous: Blackboards for Thursday November 15

Homework Assignment #7

a light one, for a change

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".

Read sections 31, 32, 33, and 35 in Munkres' textbook (Topology, 2nd edition), and if curious, also sections 9-11. 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 43 and 45, just to get a feel for the future.

Solve following problems, though submit only the underlined ones. In Munkres' book, problems 1, 5, and 6 on page 199 [note that a "closed map" is $f\colon X\to Y$ for which if $B\subset X$ is closed then $f(B)\subset Y$ is closed], problem 1 on page 205, and problems 1, 3, and 4 on pages 212-213.

In addition, if you're in the mood, very carefully read and digest the proof that the AofC is equivalent to Zorn's lemma, as written up, for example, at Zorn.html.

Due date. This assignment is due at the end of class on Thursday, November 22, 2018. If you can, please use the Homework Submission Cover Page to help with faster returns and to help with privacy.

A Lucky Break! The EGE decided to spare us until after the final! Yet:

Dire Warning. Right after Reading Week our final exam agents of the Evil Galactic Empire will lock all the students of this class in separate sound proof, electromagnetically sealed, neutrino hardened, and gravitational wave resistant rooms in the dark, cold lower basement of Sidney Smith Hall. In the rooms they will place identical countable sequences of numbered boxes, each one containing a real number (the same sequence of real numbers in each room). By Tuesday morning the day after, each student must open all but one of their boxes in the order of their liking, and guess the number in the remaining box. If more than one student will guess wrong [oh no, redacted].
Do Something! You must devise a survival strategy over reading period before the final or else we will never study the absolutely stunning Urysohn's Lemma! miss the holidays!

("Saw Omega" from Alfonso Gracia-Saz from Mira Bernstein from Vigorous Handwaving [spoilers inside]. Deadly serious.)