Last Updated：2025/11/26
Sentence
写像の下で列の収束を保証するために、距離 D_X と D_Y に関して写像 f: X → Y が任意の実数 ε>0 に対してある実数 δ>0 が存在し、X の任意の点 x, y について D_X(x,y)<δ ならば D_Y(f(x),f(y))<ε となる性質、すなわち一様連続であることを要求する。
Quizzes for review
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.
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Related words
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。
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