# Continuity of product function

Submitted by Isoscel on Thu, 11/22/2007 - 13:54.

Let f(x,y)=xy

This function is 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 to have also

used before.

As the choice of depends on the function is not uniform continuous on as it is easy to verify.