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• Topology I, spring 2010
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# Topology I, spring 2010

Juliette Kennedy

10 cu.

### Type

Basic to Intermediate studies, depending on the students' backgrounds. We start with metric spaces, progress through the basic properties of various topological spaces, i.e. Hausorff, Normal, etc. We end with Urysohn's Lemma, and the Tietze extension theorems. Our text is "Introduction to Topology and Modern Analysis" by Simmons.

### Lectures

We will have a makeup class Friday, April 16th at 16:00 in room B321.

Weeks 3-8 and 11-17 Mon 16-18 C123 and Wed 10-12 C122

Easter holiday 1.-7.4.

### Exams

Mid-term Wednesday March 17, 10-12, C323. We start at 10 sharp. For your midterm exam, you will solve/prove 5 of the following 18 problems/theorems: p.35, #2. p. 58, #1,#2. Theorems A, B, C, D, E in section 10. p. 64, #1,#4. Theorem C, section 11. p. 70, #13. Theorem B,C, D in section 12. p. 75, #5. Theorems A,C in section 13.

Final exam May 11th at 12 noon in ROOM B321. List of problems from which exam will be drawn are as follows: p. 64, #2, p. 69, #2, p. 74, prove theorem D, p. 75, #5,p. 94, #1 and #2, p. 96, prove theorem C,p. 100, prove theorems A and C (2 problems), p. 111, prove theorems A and B (2 problems)p. 121, prove theorem A, p. 124, #4, p. 123, prove theorem D, p. 135, prove theorem A.

### Registration

Did you forget to register? What to do.

### Exercise groups

Group

Day

Time

Place

Instructor

1.

Mon

12-14

C323

homework for 1.02:page 35: 2,4,6,8; page 42: 2,5; page 47: 1,2,7. Solutions here: https://wiki.helsinki.fi/download/attachments/52093428/Fansolutions1.pdf
HOMEWORK for 22.02: p. 64, 5; p. 69: 1,2,7,10,13; p. 75: 1,2. Solutions:

https://wiki.helsinki.fi/pages/viewpageattachments.action?pageId=52093428&sortBy=date&highlight=Top_Fan04.pdf&

HOMEWORK 1.03: p. 75, 1,2,5,8. Solutions:

https://wiki.helsinki.fi/pages/viewpageattachments.action?pageId=52093428&sortBy=date&highlight=Top_Fan05_3.pdf&

HOMEWORK for 31.3: page 94,: 1,9,10,11. page 98: 2,5. page 103: 3,4,6,7. Homework for 12.4: Prove the Heine-Borel Theorem (you can prove it differently from the proof of theorem G on page 114). p. 115: 5,7,8. p. 124: 1,4. p. 128: 4. Homework for 19.4: p. 131: 1,2,4,8. p. 134: 1,2.
Homework for 26.4: p. 75, 4. p.132, 3, 7. Prove the "right to left" direction of Ascoli's Theorem. Prove the "left to right" direction of Ascoli's Theorem.
Solutions: