uniformly continuous

English

1. (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 $D_X (x, y) < \delta$, it must be the case that $D_Y (f(x), f(y)) < \epsilon$ (where DX and DY are the metrics of X and Y, respectively).