MAT 3153 Assignment 2
1. p.133 # 1: Let A X. If d is a metric for the topology of X, show that d|AA is a metric
for the subspace topology on A.
2. p.152 # 4: Show that if X is an innite set, it is con
MAT 3153 Test 2
Winter 09
March 2nd
Instructor: Pieter Hofstra
Family Name:
First Name:
Student Number:
PLEASE READ THESE INSTRUCTIONS VERY CAREFULLY
You have 80 minutes to complete this exam.
This
MAT 3153 Assignment 1
1. p.20 # 2: Let f : A B, and Ai A and Bi B for i cfw_0, 1. Show that
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
B0 B1 f 1 (B0 ) f 1 (B1 ).
f 1 (B0 B1 ) = f 1 (B0 ) f 1 (B1 ).
f 1 (B0 B1 )
MAT 3153 Mid Term Exam
February 11, 2010
Duration: 80 minutes
INSTRUCTIONS: This is a closed book exam. No calculator of any sort is
allowed. Justify all your responses. You do not need to prove theor
MAT3153 Sample Problems, part 3
1. For each of the following subsets of R3 , determine whether it is compact,
locally compact, connected, path connected or locally connected:
(a) A = cfw_(x, y, z)|x|
MAT3153 Sample Problems, part 2
1. For each of the following subsets of R, determine all of the limit points of
that set:
(a) A = cfw_0
(b) B = (0, 1]
1
(c) C = cfw_ n |n N, n > 0
(d) D = Q
Solution.