1617-257/Homework Assignment 6

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Contents

Reading

Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week! Also, read, reread and rereread sections 9-10 and section 1(!) of Munkres' book to the same standard of understanding. 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 section 9, just to get a feel for the future.

Doing

Solve problems 1, 3, 5, 6 in section 9 and problems 1, 3, 4 in section 10, but submit only the underlined problems/parts. In addition, solve the following problems, though submit only your solutions of problem A:

Problem A. Find an example of a bounded continuous function on the semi-open interval (0,1] which is not uniformly continuous.

Problem B. Prove that every unbounded continuous function on the semi-open interval (0,1] is not uniformly continuous.

Submission

Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

This assignment is due in class on Wednesday November 9 by 2:10PM.

Important

Please write on your assignment the day of the tutorial when you'd like to pick it up once it is marked (Wednesday or Thursday).