# Uniformly-continuous definitions

(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 , it must be the case that (where*D*_{X}and*D*_{Y}are the metrics of*X*and*Y*, respectively).A uniformly continuous function is a function whose derivative is bounded.

adjective