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Let be X,Y metric spaces, dX,dY the metrics of X and Y. Let (fn) be a sequence of functions fn: X -> Y.
(fn) is called uniformly converging to a function f: X -> Y iff
for any u > 0, u of R there exists a n > 0, n of N with: for all x of X and all m > n dY( fm(x) , f(x) ) < u

Examples: The sequence of functions (1/n * cos(x) ) converges uniformly to the constant function f(x)=0.
The sequence of functions (xn) doesn't converge uniformly on the closed intervall (0,1)