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 connected in the nite complement
topology.
3. p.158 #2: Le
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 is a closed book exam, and no notes of any kind are all
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 ) = f 1 (B0 ) f 1 (B1 ).
f 1 (B0 B1 ) = f 1 (B0 ) f 1 (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 theorems from your notes
unless asked to do so, but you must
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| + |y| + |z| < 1
(b) B = cfw_(x, y, z)|x2 + y 2 + z 2 =
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.
A = : 0 is not a limit point, because if U is an open
n
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