Uniformly continuous

English

Adjective

1. Template:Lb 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 $D_X(x,y)<\delta$, 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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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

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Translations

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