The University of Colorado

Boulder, Colorado

Mathematics 6210, Fall 2002

Introduction to topology (graduate level)

Location:
Schedule: none. (Class over.)
Professor: Walter Taylor
- Email address: walter.taylor@colorado.edu
- Office Phone: (303) 492-8344 (Please email if at all possible)
- Office : Mathematics Building 255
Office hours:
- Regular hours: none (class over)
- Other times can be arranged by email or simply by checking if I am available at a given time.
Attendance: To be considered properly enrolled in the course, you must have this hour free on all MWF-days. At no time will I accommodate anyone who has registered for the class with a schedule conflict, academic or otherwise, or anyone who attempts to do so.
You are expected to be in class every day. On the other hand, if you need to miss one class, on a day when there is no exam, just do it. (In such a case, permission from me is irrelevant.) I am happy to tell you in general terms what we covered in a class you missed. Nevertheless, I really cannot begin to recreate a class situation for you, since much of the material is spontaneous, and depends on student participation.
Class decorum: No eating. No drinking. No reading of newspapers, etc. No conversation or talking. No exceptions. If you need to do any of these things, please leave the room; I will not be offended. It is of course an absolute no-no to have your cell phone ring during class!

This page pertains only to Professor Taylor's section of Mathematics 6210, for the fall semester of 2002. As far as I know, this is the only section occurring this semester. For other sections or other semesters, other details and regulations will no doubt apply.

An attempt will be made to keep this page up-to-date, but this is not guaranteed. Students are responsible for every assignment made in class, whether or not it ultimately appears on this page.

Textbook

Topology, Second Edition, by James R. Munkres, ISBN 0-13-181629-2

About homework

There will be several sets of homeworks during the semester. Generally they will be taken from the book. Although this is a course about topology and its role in mathematics, it is also a course about proofs . We are learning to be mathematicians! (If this doesn't appeal to you, don't enroll!) Therefore the homeworks will often be small proofs that are accessible at our level. Unless there is a huge enrollment, I will read all the homeworks myself, and offer suggestions for correction.

Up to three HW papers may be turned in for an improved score. The deadline is the start of the last class period (Dec. 11). It will help me if you include your old work, so I can figure out how much was previously deducted. Your write up should include a complete re-statement and re-solution of any HW problem for which you wished enhanced credit. Do not include a re-write-up of those problems that were previously accepted as correct.

Exams

You must be present at all exams.
No books, calculators, cards or other aids.
Hour exams are in the usual classroom, at the usual class time, and are limited to the usual fifty-minute hour.
- First Hour Exam: Wednesday, October 9, 2002.
- Make-up of first Hour Exam: Monday, October 21, 2002.
- Second Hour Exam: Wednesday, November 13, 2002
- Third Hour Exam: Wednesday, December 11, 2002
- No exam during the post-class "final exam period."

Homework.

HW 1, Due Friday, September 6
- p. 51 -- 1, 6
- p. 61 -- 2cd, 5
- p. 66 -- 2, 3, 4, 5, 6, 7
HW 2, Due Monday, September 16
- p. 83 -- 4a, 5, 6, 8
- p. 91 -- 1, 2, 3, 6, 8, 9
HW 3, Due Friday, September 20
- p. 100 -- 5, 6, 9, 10, 11, 14
- p. 112 -- 3, 6
HW 4, Due Friday, September 27
- p. 112 -- 9bc, 12, 13
- p. 118 -- 6, 7, 8
HW 5, Due Friday, October 4
- p. 126 -- 1a, 2, 4, 5
- p. 133 -- 1, 3a, 4, 10
HW 6, Due Friday, October 18
- p. 152 -- 1, 3, 5, 7, 8, 10
- p. 157 -- 1a, 2, 4
HW 7, Due Friday, October 25
- p. 157 -- 6, 12 (a long exercise about the long line)
- p. 170 -- 1, 4, 5
HW 8, Due Friday, November 1
- p. 170 -- 8, 11
- p. 177 -- 4, 5, 6
HW 9, Due Friday, November 8
- p. 181 -- 2, 3c, 4, 6
- p. 186 -- 1, 4, 6
- p. 187 -- 6
HW 10, Due Friday, November 22
- p. 71 -- 4, 6
- p. 194 -- 4, 8, 9
- p. 199 -- 2, 4
- p. 235 -- 1, 3b (Note. In part (c) of 1, you must assume that X is Hausdorff, not merely T₁. This is the only mistake that I have detected in Munkres.)
HW 11, Due Friday, December 6
- p. 205 -- 4, 5, 7 (use 6 if you like)
- p. 212 -- 7
- p. 218 -- 2, 4
- p. 223 -- 3 (we may not have proved Tietze's Thm; feel free to use it anyway)
- p. 227 -- problems deleted
- p. 241 -- 4, 5

The normal Moore space conjecture

For a good exposition, see this review and article by Dow, Tall and Weiss, 1992. (If that doesn't work, go here and click on article 44.)