University of Louisiana at Lafayette, Math 536, Topology II

  • 1/22/08 Homework: the problem stated in today's lecture, pg. 186: 5.
  • Note: here is the course info sheet.
  • 1/24/08 Homework: pg. 186: 10.
  • 1/29/08 Homework: (1) Here is the problem discussed in class today. This is due the first Tuesday after Mardi Gras. You should write 3/4ths of a page. I look forward to reading and, perhaps, learning some interesting topology. Your work will be graded out of 10 points on the basis of your work's "research quality." (2) pg. 194: 11 - this problem answers a question that Jake asked today.
  • 2/1/08 Homework: due the first Tuesday after Mardi Gras: pg. 199: 8. (Next Thursday, we begin with Section 32.)
  • 2/7/08 Homework (due next Thursday): Section 32: 1, 4.
  • 2/12/08 Homework: Section 32: 3, 6.
  • 2/14/08 Homework: Section 33: 2, 6a.
  • 2/19/08 Homework: carefully read the proof of Theorem 35.1; we will state this result in class, but not take the time to do the proof (since much of the proof is analysis).
  • 2/21/08 Homework: Section 35: 1, 5.
  • 2/26/08 Homework: Section 36: 1, 4.
  • 2/28/08 Homework: Section 37: 1, 2.
  • 3/4/08 Homework: (The following problem could have been assigned before today's lecture.) Let X be a space that is non-compact, locally compact, and Hausdorff. Show that if the one-point compactification of X is metrizable, then X is second countable.
  • 3/6/08 Homework: As mentioned in class, go through the proof of Theorem 38.5. Read the definition that concludes Section 38. Section 38: 4 - together with an explanation of the meaning of the second sentence of the bracketed remarks, 6, 10.
  • 3/11/08 Homework: In today's class, we concluded that 3b, from the first edition of Munkres, could be proven by running through Sieradski's proof of 4.7. But we were left with a gap in that we did not fully understand the last two lines of the proof. Give a complete verification of these last two lines.
  • 3/13/08 Homework: none for today.
  • 3/13/08 impromptu Moore method day three: after today's class, you are responsible for the following: the definition on the first page of \S 39, lemma 39.1 and its proof, the first definition on the second page of \S 39, the second definition on the second page of \S 39, read and familiarize yourself with the statement of Lemma 39.2, study the definition of the metric topology that is known as the uniform topology, the only definition on the second page of \S 40, lemma 40.1 and its proof, read and familiarize yourself with theorem 40.3, ... on Tuesday, we begin \S 41.
  • 3/18/08: After today, you are responsible for Section 41 through the end of Example 3, the statements of Theorems 41.4 and 41.5, the facts in Examples 4-6.
  • 3/20/08 Homework: review Theorem 41.8 and go over the proof. The following problem is due on Thursday after break - it's not an easy problem. Let X be a space such that each countable open covering of X has a finite subcovering. Show that if X is paracompact and Hausdorff, then it is compact. (This problem is worth ten points.)
  • 4/1/08 Homework: Section 46: 6.
  • 4/3/08 Homework: the homework problem given in class today related to the claimed adjunction (since I didn't write down the problem or the notation that I used on the board, write your solution so that it explains what any notation means), Section 51: 1.
  • 4/8/08 Homework: Section 51: 2, 3ab.
  • 4/10/08: Here is the midterm exam.
  • 4/15/08 Homework: Section 52: 4, 6.
  • 4/17/08 Homework: for Section 52, 7, do the following: don't work it out and turn in nothing; read it carefully; think about all the elegant ideas that are present in the statements; realize that there is algebra in the topology and this algebra is inducing algebraic structure on the set of loops and on the fundamental group; see that some of the algebraic structure of the fundamental group reflects the algebra in the topology; note that the algebraic structure of the fundamental group has a nice algebraic property that the topology does not have. Section 53: 2; read, but don't turn in, 3; 6b (if necessary, you may use the paragraph that precedes Example one).
  • 4/22/08 Homework: Section 54: 3, 4.
  • 4/24/08 Homework: Section 54: 6, 8.
  • 4/29/08 Homework: Section 54: 7.
  • 5/1/08 Homework (due Thursday): Section 55: 1, 2.
  • 5/6/08 Homework (due Tuesday): Here is the homework assignment.
  • 5/16/08: Here is the final exam.
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