Adjective
uniformly continuous (not comparable)
(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
{\displaystyle D_{X}(x,y)<\delta }
, it must be the case that
D
Y
(
f
(
x
)
,
f
(
y
)
)
<
ϵ
{\displaystyle D_{Y}(f(x),f(y))<\epsilon }
(where DX and DY are the metrics of X and Y, respectively).
A uniformly continuous function is a function whose derivative is bounded.