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Lebl-Basic-Analysis-I
· Problem 7.5.5
Metric Spaces
Mathematics · continuous-functions
Problem
Suppose
f
:
X
→
Y
f \colon X \to Y
f
:
X
→
Y
is continuous for metric spaces
(
X
,
d
X
)
(X, d_X)
(
X
,
d
X
)
and
(
Y
,
d
Y
)
(Y, d_Y)
(
Y
,
d
Y
)
. Show that if
X
X
X
is connected, then
f
(
X
)
f(X)
f
(
X
)
is connected.
Related theory
Characteristic Functions And Moment Generating Functions
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