Math 54
Topology I
Last updated June 17, 2015 12:57:08 EDT

Announcements:

• The first meeting is Friday, June 22nd.
• We also have class on Saturday, June 23rd.
• The grading scale for the first three homework assignments. To be updated with release of new assignments.

### Homework Assigments

Week of June 18 - 22, 2012
 Monday: Study: No class Do: Wednesday: Study: No class. Maybe crack open Munkres' book. Do: Friday: Study: 1.1-1.3. Do: (Problem Y in section X is denoted X.Y) Write up for turning in: 1.1,1.3,2.2,4.4,6.2. Also turn in a proof that if x is an element of Euclidean n-space, and epsilon > 0, then the ball of radius epsilon about x is an open set. You may use the fact that for a,b points in n-space ||a+b|| \leq ||a|| + ||b|| (\leq means less than or equal to). Solve, but DON'T turn in: 1.7,2.5,5.1,6.5 (this one is mildly devious). We will discuss these on Tuesday in x-hour and then you will turn them in on FRIDAY (the 29th). [note: previously asked for 4.13 but does not anymore.] Solutions for Homework 1 .
Week of June 25 - 29, 2012
 Monday: Study: 2.12-13 Do: 13.1, 13.3, 13.4, 13.6, 13.7 (These will be due Tuesday, July 3). Solutions for these and those assigned on Friday. Wednesday: Study: 2.13 Do: Friday: Study: 2.14-16. Do: 16.1,16.2,16.4,16.8 (depends on the slope of the line). These are due Tuesday, July 3.
Week of July 2 - 6, 2012
 Monday: Study: 2.17 Do: 17.1, 17.3, 17.6-11, 17.13. These are due July 10th. We will talk about Hausdorff spaces on Friday, July 6th. Solutions Wednesday: Study: Fireworks. Do: Have Fun. Friday: Study: 2.17 - Hausdorff spaces. 2.18 Do:
Week of July 9 - 13, 2012
 Monday: Study: 2.18 Do: (18.2), 18.3, 18.4, 18.5, 18.7a(b), 18.8, 18.10, 18.12, (18.13). Do not turn in the problems listed in parentheses (solve them anyway, for maximum effect). The rest are due July 17th. For: 18.7a, use the definition of right-continuity listed in this Wikipedia article. Solutions Wednesday: Study: 2.19 Do: 19.1, 19.3, 19.6, 19.10. (For Tuesday, July 17th). Solutions Friday: Study: 2.19-20. Do:
Week of July 16 - 20, 2012
 Monday: Study: 2.20 Do: 20.1a, 20.3, 20.9, 20.11, 21.2, 21.3a, 21.12. For 20.11 you can ignore the word "bounded" and you can use this supplementary hint: the function f(x) = x/(1+x) = 1-(1/(1+x)) is increasing on the interval [0,infty). Make sure to prove the hint is true if you reference it in your solution. (Due July 24th). Wednesday: Study: For the exam (covers through universal mapping property of the product). Do: Friday: Study: Do:
Week of July 23 - 27, 2012
 Monday: Study: 3.23, 3.24 Do: 23.1, 23.2, 23.3, 23.5, (23.7), 23.9, 23.10, 24.1, (24.2), 24.3, 24.7ab, 24.10. Don't need to turn in 23.7, 24.2, or 24.7c. These are due on the 31st. Wednesday: Study: 3.23, 3.24, 3.26, 3.27. Do: Friday: Study: 3.26-28. Do:
Week of July 30 - Aug 3, 2012