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

General Information Syllabus HW Assignments


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Homework Assigments

Week of June 18 - 22, 2012
Assignments Made on:
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
Assignments Made on:
Monday:
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
Assignments Made on:
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
Assignments Made on:
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
Assignments Made on:
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
Assignments Made on:
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
Assignments Made on:
Monday:
  • Study: 3.26,3.27,3.29.
  • Do: 26.1, 26.5, 26.7, 26.8 (Due Tuesday, August 7th).
Wednesday:
  • Study: 3.29. PAY SPECIFIC ATTENTION TO: The statement and proof of Theorem 29.1. It will be extremely useful to us next week.
  • Do: 27.6 (Due Tuesday, August 7th). The exam is on August 8th.
Friday:
  • Study: 4.30..
  • Do:
Week of Aug 6 - Aug 10, 2012
Assignments Made on:
Monday:
  • Study: 4.30-4.32
  • Do: 30.3, 30.9 (think about a problem from section 16), 30.12, 31.1, 31.3 (Do not use the fact, alluded to by Munkres, that every order topology is normal), 31.5.
Wednesday:
  • Study: For the exam.
  • Do: The exam.
Friday:
  • Study: 4.32,4.33, 2.20, 2.21
  • Do:
Week of Aug 13 - Aug 17, 2012
Assignments Made on:
Monday:
  • Study: 4.32,4.33
  • Do: 32.1, 32.4, 32.6, 33.2 (Hints: for (a): remember a remarkable theorem about the image of a connected space; for (b): a previous problem on this assignment), 33.3 (p.175 for the definition of d(x,A), 34.3 (You can cite, without proof, problems from section 30 as well as this section).
Wednesday:
  • Study: 4.33, 4.34.
  • Do:
Friday:
  • Study: 4.34, 4.35.
  • Do:


Dan Crytser
Last updated June 17, 2015 12:57:08 EDT