Topology I, spring 2010
Lecturer
Scope
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.
Prerequisites: Single and Multivariable Calculus
Lectures
We will have a makeup class Friday, April 16th at 16:00 in room B321.
Weeks 38 and 1117 Mon 1618 C123 and Wed 1012 C122
Easter holiday 1.7.4.
Exams
Midterm Wednesday March 17, 1012, 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.
Bibliography
Registration
Did you forget to register? What to do.
Exercise groups
Group 
Day 
Time 
Place 
Instructor 


1. 
Mon 
1214 
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 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 HeineBorel 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. , https://wiki.helsinki.fi/download/attachments/52093428/Top_Fan07_2.pdf. Solutions, last set: /wiki.helsinki.fi/download/attachments/52093428/Top_Fan09_31.pdf 