MATH 3220
THIRD HOMEWORK ASSIGNMENT
Sept. 12, 2000
A. Treibergs
Due Sept. 19, 2000
Please write up the following exercises from the text "Introduction to Analysis, Second Edition" by William Wade, Prentice Hall 1999.
259[ 1, 3, 4, 7, 10cd ].
Here are the equivalent exercises for those using the First Edition:
231[3,4,9],
Find the interior, closure, and boundary of the following subsets of
R
.
[
a, b
) where
a < b
.
E =
{
1 / n : n €
N
}
.
E =
U
n€
N
(
2
-n-1
, 2
-n
)
.
E =
U
n€
N
(
-n, n
)
.
Let
A, B
be substs of
R
n
. Prove that
d( A « B) Ã ( A « dB) » (dA « B) » (dA « dB)
.
∂( A ∩ B) ⊂ ( A ∩ ∂B) ∪ (∂A ∩ B) ∪ (∂A ∩ ∂B)
.