##  [Uniform Continuity](/uniform-continuity) 

  ##  [Uniform Continuity](https://puremath.quantumdictionary.io/uniform-continuity-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Global version of continuity: a function f on a domain D is uniformly continuous if for every ε>0 there exists a single δ>0 such that for all x,y in D, d(x,y)<δ implies d(f(x),f(y))<ε. The key is that δ depends only on ε, not on the point.