uniformly continuous

adjective

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, 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).

“A uniformly continuous function is a function whose derivative is bounded.”

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Meanings

adjectiveuniformly continuous (not comparable)
  1. not comparablemathematical analysisThat 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, 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).

    A uniformly continuous function is a function whose derivative is bounded.

Translations

Bulgarian равномерно непрекъснат
  • равномерно непрекъснат (ravnomerno neprekăsnat)property of a function
French uniformément continu
  • uniformément continuproperty of a function
German gleichmäßig stetig
  • gleichmäßig stetigproperty of a function
Hungarian egyenletesen folytonos
  • egyenletesen folytonosproperty of a function
Icelandic samfelldur í jöfnum mæli
  • samfelldur í jöfnum mæliproperty of a function
Polish jednostajnie ciągły
  • jednostajnie ciągłyproperty of a function
Swedish likformigt kontinuerlig
  • likformigt kontinuerligproperty of a function
Cite this entry
APA

uniformly continuous. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/uniformly%20continuous

MLA

“uniformly continuous.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/uniformly%20continuous. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “uniformly continuous,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/uniformly%20continuous.

Source: uniformly continuous on Wiktionary, CC BY-SA 4.0.