10-327/Homework Assignment 4

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Contents

Reading

Read sections 23 through 25 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 26 through 27, just to get a feel for the future.

Doing

Solve and submit problems 1-3 and 8-10 Munkres' book, pages 157-158.

Due date

This assignment is due at the end of class on Monday, October 25, 2010.

Suggestions for Good Deeds

Annotate our Monday videos (starting with Video: dbnvp Topology-100927) in a manner similar to (say) dbnvp AKT-090910-1, and/or add links to the blackboard shots, in a manner similar to dbnvp Alekseev-1006-1. Also, make constructive suggestions to me, Dror and / or the videographer, Qian (Sindy) Li, on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relatively easily in the real world, given limited resources".

Dror's notes above / Student's notes below

Questions

1)Hi, quick question. I am wondering if the term test will cover the material on this assignment, or only the material before the assignment. Thanks! Jason.

2) In EXAMPLE 7 on page 151 Munkres claims that Rn~ is ['clearly' :)] homeomorphic to Rn: where Rn~ consists of all sequences x=(x1,x2,x3,...) with xi=0 for i>n, and Rn consists of all sequences x=(x1,x2,...xn). Why are they homeomorphic ?? Thank you kindly. Oliviu.