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Lebl-Basic-Analysis-I
· Problem 3.4.7
Continuous Functions
Mathematics · uniform-continuity
Problem
Let
f
:
(
0
,
1
)
→
R
f : (0, 1) \to \mathbb{R}
f
:
(
0
,
1
)
→
R
be a bounded continuous function. Show that the function
g
(
x
)
:
=
x
(
1
−
x
)
f
(
x
)
g(x) := x(1-x)f(x)
g
(
x
)
:=
x
(
1
−
x
)
f
(
x
)
is uniformly continuous.
Related theory
uniform-continuity
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