uniformly continuous

English

Adjective

uniformly continuous (not comparable)

1. (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 $D_{X}(x,y)<\delta$, it must be the case that $D_{Y}(f(x),f(y))<\epsilon$ (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.

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

property of a function

• French: uniformément continu
• German: gleichmäßig stetig
• Hungarian: egyenletesen folytonos
• Icelandic: samfelldur í jöfnum mæli m
• Mongolian: жигд тасралтгүй (žigd tasraltgüj)
• Polish: jednostajnie ciągły
• Serbo-Croatian:

  Cyrillic: (Ijekavian) ра̏вномјерно не̏прекӣдан, (Ekavian) ра̏вномерно не̏прекӣдан, једно̀лико не̏прекӣдан, у̀нифо̄рмно не̏прекӣдан

  Roman: (Ijekavian) rȁvnomjerno nȅprekīdan, (Ekavian) rȁvnomerno nȅprekīdan, jednòliko nȅprekīdan, ùnifōrmno nȅprekīdan

• Swedish: likformigt kontinuerlig (sv)