Uniform continuity of a map 
from a metric space 
to a metric space 
means that for every 
, there exists a 
such that 
whenever 
satisfy 
.
The value of 
may depend on 
and 
,
but it is independent of the points 
and 
. Uniform continuity is therefore stronger than continuity;
every uniformly continuous function is continuous.
Examples include Lipschitz functions and functions satisfying a Hölder
condition. Not every continuous function
is uniformly continuous: for example, 
on 
and 
on 
are not. Every function continuous
on a compact domain is
uniformly continuous.
