Topology I, fall 2008
Topology I, fall 2008
Lecturer
Scope
10 sp.
Type
Intermediate studies.
Lectures
Weeks 36-42 and 44-50, Monday 10-12 and Wednesday 10-12 in room B322.
Contents
We cover the basic theory of metric spaces before going on to topological spaces. Time permitting we will try to reach Ascoli's Theorem, Urysohn's Lemma and the Tietze Extension Theorem.
Course material
The text is: "Introduction to Topology and Modern Analysis" by Simmons.
A copy of the relevant parts of the text is available in room C326 (third floor; look for the notebook corresponding to Topology 1, fall 2006). THE TEXT FOR WEEKS 36 AND 37 IS LIPSCHUTZ'S GENERAL TOPOLOGY. PROBLEMS ASSIGNED REFER TO THIS TEXT. AFTER WEEK 37 WE WILL USE SIMMONS. LOOK FOR LIPSCHUTZ ON THE 3RD FLOOR STARTING TOMORROW, THURSDAY SEPTEMBER 4.
Registration
Final Exam: Monday, December 15, 10-12, B322. NOTE NEW EXAM TIME. WE BEGIN AT 10 SHARP. URYSOHN'S LEMMA IS NOT ONE OF THE QUESTIONS. THEOREM 1 PAGE 130 IS ON THE LIST INSTEAD.
Exercise groups
Group | Day | Time | Place | Instructor |
|---|---|---|---|---|
1. | Mon | 14 - 16 | B321 | Ari Adjangba |
Exercises
Week | Exercises |
|---|---|
36 | Page 24, problems 5 and 6. Page 26, prob 12 and 16. P29, prob 29 and 39, P30, prob 41 |
37 | ALL EXERCISES FROM NOW ON ARE FROM SIMMONS: Page 20, problem 6. Prove the Schroder-Bernstein Theorem (see p.29). Prove the properties (1) on p. 18. |
38 | Page 59, problem 6. Page 64, prob 1-5, 8,9 and 10. P69, prob 1-4,6 |
39,40 | Page 68, prove property 3. Page 69, prove properties 1-3. Page 69, problem 2,7,9,13 . EXERCISES WEEK 41: p.75, problem1,2,7,8. |
41 | p.75, 1,2,5. p.79, 1,2,4. |
43 | p.80: 3,9. p.84: 3,4,5a-5d. p.90:3 |
44 | EXAMPLE CLASS IS CANCELLED THIS WEEK. (So no class November 2nd.) |
45 | p.94, 2,4,7. p.98, 1,3,6. p.104, 9. |
46 | p.103, 69. p.109, 2. p.114, 4,7,8. |
47 | p.114, 1,3,5,7. p.124, 4. |
48 | p. 115, 8. p.124, 1. p.128, 1,4. |
49 | p.131, 12,3,8a-8c |