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

(6)

Next: Blackboards for Tuesday September 18
Previous: Blackboards for Thursday September 13

Homework Assignment #1

Read sections 12 through 16 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 17 through 20, just to get a feel for the future.

Solve and submit the following problems. In Munkres' book, problems 1, 3, 4, and 8 on pages 83-84, and the following extra problem:

Extra Problem. Prove that a function $f\colon X\to Y$ is continuous, where both $X$ and $Y$ are taken with the finite-complement ("fc") topology, if and only if it is constant or finite-to-one. ("Finite-to-one" means that any $y\in Y$ has at most finitely many inverse images: $\forall y\in Y\ |f^{-1}(\{y\})|<\infty$).

Due date. This assignment is due at the end of class on Thursday, September 20, 2018.