Phrase guide

uniformly continuous

adj · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

adj

Meaning 1

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).

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: mathematical-analysis, mathematics, sciences

Examples

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

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

16 source translations are retained for this English entry.

  • Bulgarian: равномерно непрекъснат (ravnomerno neprekǎsnat) — property of a function
  • French: uniformément continu — property of a function
  • German: gleichmäßig stetig — property of a function
  • Hungarian: egyenletesen folytonos — property of a function
  • Icelandic: samfelldur í jöfnum mæli — property of a function
  • Mongolian: жигд тасралтгүй (žigd tasraltgüj) — property of a function
  • Polish: jednostajnie ciągły — property of a function
  • Serbo-Croatian: ра̏вномјерно не̏прекӣдан — property of a function
  • Serbo-Croatian: ра̏вномерно не̏прекӣдан — property of a function
  • Serbo-Croatian: једно̀лико не̏прекӣдан — property of a function
  • Serbo-Croatian: у̀нифо̄рмно не̏прекӣдан — property of a function
  • Serbo-Croatian: rȁvnomjerno nȅprekīdan — property of a function
  • Serbo-Croatian: rȁvnomerno nȅprekīdan — property of a function
  • Serbo-Croatian: jednòliko nȅprekīdan — property of a function
  • Serbo-Croatian: ùnifōrmno nȅprekīdan — property of a function
  • Swedish: likformigt kontinuerlig — property of a function