# Uniform continuity of sum function

Submitted by Structure on Wed, 11/21/2007 - 22:47.

Let f(x,y)=x+y

This function is uniform continuous, as it is easy to verify using "Continuous Function on metric space"previous criteria.

Let and let for all such as we have

and the last product is less or equal to if So we can chose

As the choice of does not depend on the function is uniform continuous on