Math 4A03: Assignment 4
Due Tuesday, November 2 by 11:00 am
Total of Marks= 50
Problem 1. [10 marks] Let cfw_fn (x)n1 be a sequence of functions in C([0, 1])
and suppose that fn f uniformly on [0, 1]. Show directly, i.e. without using
the generalized Hein

LAST (family) NAME:
Test # 2
FIRST (given) NAME:
Math 4A03
ID # :
November 17, 2010
Instructor:
Dr. J.-P. Gabardo
Instructions: You must use permanent ink. Tests submitted in pencil will not be considered
later for remarking. This test consists of 6 probl

Math 4A03: Assignment 2: SOLUTIONS
Due Friday, October 22 by 11:00 am
Total of Marks= 50
Problem 1. [5 marks] Find an explicit example of a metric d on R for which
(R, d) is not complete.
Solution. We can, for example, define
d(x, y) = |ex ey | ,
x, y R.

Math 4A03: Assignment 6
Due Tuesday, November 30 by 11:00 am
Total of Marks= 50
Problem 1. [5 marks] # 20 om p. 349.
Solution. We first show that f is locally constant, i.e. that if p U and the
ball Br (p) = cfw_x Rn , |x p| < r U , then f (q) = f (p) for

Math 4A03: Assignment 5: SOLUTIONS
Due Tuesday, November 16 by 11:00 am
Total of Marks= 50
Problem 1. [10 marks] Let f : [0, 1] R be continuous.
(a) Find necessary and sufficient conditions on the function f (x) guaranteeing
that the collection of functio

Math 4A03: Assignment 1: SOLUTIONS
Due Tuesday, September 28 by 11:00 am
Total of Marks= 50
Problem 1. [10 marks] Let (an )n1 be a sequence of real numbers and assume
that, for every integer k 2, we have
lim akn = 0.
n
Can we conclude that limn an = 0? Ei

LAST (family) NAME:
Test # 1
FIRST (given) NAME:
Math 4A03
ID # :
October 20, 2010
Instructor:
Dr. J.-P. Gabardo
Instructions: You must use permanent ink. Tests submitted in pencil will
not be considered later for remarking. This test consists of 5 proble

Math 4A03: Assignment 3: SOLUTIONS
Due Friday, October 22 by 11:00 am
Total of Marks= 50
Problem 1. [15 marks] # 54 on p.121
Solution. The interior of a connected set need not be connected. For example, consider the set A consisting of the union of the cl