Math 508
Exam 2
Jerry L. Kazdan
December 4, 2008
10:30 – 11:50
Directions
This exam has two parts, Part A has 10 TrueFalse problems (30 points, 3 points
each). Part B has 5 traditional problems (70 points, 14 points each).
Closed book, no calculators or computers– but you may use one 3
00
×
5
00
card with notes on both
sides.
Part A: True/False
(answer only, no reasons). 10 problems, 3 points each).
Circle
T
or
F
in in each problem.
1.
T
F
A bounded sequence
{
a
n
}
of real numbers always has a convergent subsequence.
2.
T
F
A series
∑
∞
n
=1
a
n
of complex numbers converges if and only if the corresponding
sequence of partial sums is bounded.
3.
T
F
A closed and bounded subset of a complete metric space must be compact.
4.
T
F
If
A
and
B
are compact subsets of a metric space, then
A
∪
B
is also compact.
5.
T
F
If
M
is any metric space and
f
:
M
→
R
is any continuous realvalued function,
then the function
g
:
M
→
R
defined by
g
(
x
) := (
f
(
x
))
2
is always continuous.
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 Fall '10
 STAFF
 Math, Topology, Metric space, Compact space, Jerry L. Kazdan

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