The difference between uniform continuity and (ordinary) continuity is that, in uniform continuity there is a globally applicable (the size of a function domain interval over which function value differences are less than ) that depends on only , while in (ordinary) continuity there is a locally applicable that depends on both and . So uniform continuity is a stronger continuity condition than continuity; a function that is uniformly continuous is continuous but a function that is continuous is not necessarily uniformly continuous. The concepts of uniform continuity and continuity can be expanded to functions defined between metric spaces.
The difference between uniform continuity and (ordinary) continuity is that in uniform continuity there is a globally applicable (the size of a function domain interval over which function value differences are less than ) that depends on only  while in (ordinary) continuity there is a locally applicable that depends on both and  So uniform continuity is a stronger continuity condition than continuity; a function that is uniformly continuous is continuous but a function that is continuous is not necessarily uniformly continuous The concepts of uniform continuity and continuity can be expanded to functions defined between metric spaces