Uniformly Cauchy sequence
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In mathematics, a sequence of functions {fn} from a set S to a metric space M is said to be uniformly Cauchy if:
- For all
and for all 
, there exists N > 0 such that 
whenever m,n > N.
Another way of saying this is that 
as 
, where the uniform distance du between two functions is defined by
[edit] Generalization to Uniform spaces
A sequence of functions {fn} from a set S to a metric space U is said to be uniformly Cauchy if:
- For all and for any entourage
, there exists N > 0 such that 
whenever m,n > N.
