# 10-327/Homework Assignment 5

Read sections 26 and 27 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 28 and 29, just to get a feel for the future.

### Doing

Solve the following problems from Munkres' book, though submit only the underlined ones: Problems 1, 4, 5, 6, 7, 8, 9, 12 on pages 170-172, and problem 2 on page 177. (For the last, recall that $d(x,A):=\mbox{inf}_{a\in A}d(x,a)$).

### Due date

This assignment is due at the end of class on Thursday, November 11, 2010.

 Dror's notes above / Student's notes below
• Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
• Indeed so, though usually when talking about boundedness, people use the letter $M$ and not the letter $\epsilon$. It makes no difference, of course.