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Lebl-Basic-Analysis-I
· Problem 7.5.3
Metric Spaces
Mathematics · continuous-functions
Problem
Suppose
(
X
,
d
X
)
(X, d_X)
(
X
,
d
X
)
,
(
Y
,
d
Y
)
(Y, d_Y)
(
Y
,
d
Y
)
are metric spaces and
f
:
X
→
Y
f \colon X \to Y
f
:
X
→
Y
is continuous. Let
A
⊂
X
A \subset X
A
⊂
X
. a) Show that
f
(
A
‾
)
⊂
f
(
A
)
‾
f(\overline{A}) \subset \overline{f(A)}
f
(
A
)
⊂
f
(
A
)
. b) Show that the subset can be proper.
Related theory
Characteristic Functions And Moment Generating Functions
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