Topology
Homework #3. Due Monday, October 2, before the lecture.
Read 14, 26, the first half of 27, and do the following problems.
Exercises 2a and 3 on page 171.
In exercises 1, 2 and 3 below do not justify your answers.
1. Which of the following subsets
Topology
Homework #6. Due Monday, October 30, before the lecture.
, 3 , 4.
1. (a) Compute 5-adic norms of 225, 6
15 467
(b) Find 5-adic expansions of
1
3
and 45 .
2. Which of the following sequences cfw_xn are Cauchy in Q with
respect to the 7-adic metri
Topology
Homework #9.
ture.
Due Wednesday, November 29, before the lec-
1. Show that each of the following is a retract of the disk D:
(a) any diameter of D;
(b) any closed interval in D.
2. What is the fundamental group of each of the following spaces?
(
Topology
Homework #4. Due Monday, October 9, before the lecture.
Read 23, 24 and the first half of 27. See 3 for the definition the
least upper bound property, needed in 24.
Do the following problems.
Exercises 1, 4, 9, 7 on page 152.
Exercises 1, 8, 9 on
Topology
Homework #8. Due Monday, November 20, before the lecture.
Exercise 2abc on page 177.
Exercises 1, 2a, 3ab on page 330.
Exercise 1 on page 334.
Exercises 1 and 5 on page 341.
Topology
Homework #1. Due Monday, September 18, before the lecture.
Read the following parts of Chapter 2: 12, 13, 15, 17 and the
first half of 16.
Solve the following problems:
Exercises 2, 7 and 8a on page 83 of the textbook (skip T2 in exercise
7).
Exe
Topology
Homework #2. Due Monday, September 25, before the lecture.
Read 17 and 18 and do the following problems.
Exercises 2, 6, 15, 19, 20 on pages 100102.
Exercises 2, 3, 7a, 10, 13 on pages 111112.
Topology
Homework #10.
ture.
Due Wednesday, December 6, before the lec-
Exercises 2, 3, 4 on page 366.
Exercise 1 on page 375.
1. Simplify the following elements of the free group Z Z:
ab2 a1 ab2 a1 ,
(ab2 a1 )50 ,
(aba2 b2 )1 aba2 .
Topology
Homework #7. Due Wednesday, November 8, before the lecture.
Exercise 4 on page 92.
1. (a) Show that a continuous map f : X Y is open if, for some
basis B of X, the set f (U ) is open in Y for any U B.
(b) Give an example of a continuous surjectiv
Topology
Homework #5. Due Monday, October 16, before the lecture.
Read 20, 21, the first half of 25, and do the following problems.
Exercises 2 and 4 on page 127.
Exercise 1 on page 133.
1. Write down all letters of the alphabet, in capitals. Group the
le
