Last Updated
：2025/11/26
uniformly continuous
Adjective
not-comparable
of a function from a metric space X to a metric space Y
(mathematical
analysis,
of
a
function
from
a
metric
space
X
to
a
metric
space
Y)
That
for
every
real
ε
>
0
there
exists
a
real
δ
>
0
such
that
for
all
pairs
of
points
x
and
y
in
X
for
which
D_X(x,y)<𝛿,
it
must
be
the
case
that
D_Y(f(x),f(y))<𝜀
(where
D_X
and
D_Y
are
the
metrics
of
X
and
Y,
respectively).
Japanese Meaning
数学的解析において、ある関数 f: X → Y が一様連続であるとは、任意の実数 ε > 0 に対して、ある実数 δ > 0 が存在し、空間 X の任意の 2 点 x, y について、もし X 上の距離 Dₓ(x, y) が δ 未満ならば、Y 上の距離 Dᵧ(f(x), f(y)) が ε 未満となるという性質を意味する。
Sense（1）
(mathematical
analysis,
of
a
function
from
a
metric
space
X
to
a
metric
space
Y)
That
for
every
real
ε
>
0
there
exists
a
real
δ
>
0
such
that
for
all
pairs
of
points
x
and
y
in
X
for
which
D_X(x,y)<𝛿,
it
must
be
the
case
that
D_Y(f(x),f(y))<𝜀
(where
D_X
and
D_Y
are
the
metrics
of
X
and
Y,
respectively).
Quizzes for review
(mathematical analysis, of a function from a metric space X to a metric space Y) That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<𝛿, it must be the case that D_Y(f(x),f(y))<𝜀 (where D_X and D_Y are the metrics of X and Y, respectively).
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See correct answer
uniformly continuous
To guarantee the convergence of sequences under the mapping, we require the function f: X → Y to be uniformly continuous with respect to the metrics D_X and D_Y.
See correct answer
To guarantee the convergence of sequences under the mapping, we require the function f: X → Y to be uniformly continuous with respect to the metrics D_X and D_Y.
音声機能が動作しない場合はこちらをご確認ください
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