uniformly continuous

== English == === 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). ==== Usage notes ==== This property is, by definition, a global property of the function's domain. That is, there is no such thing as "uniform continuity at a point," since the choice of δ for a given ε does not depend on where the points x and y are located in X. ==== Related terms ==== uniform continuity ==== Translations ====