Uniformly continuous mappings

[dan323]

We need a theory of uniformly continuous mappings to really manage the structure of uniformities:

• During the rest of the steps, prove some useful lemmas about (fxg):AxC->BxD the product of 2 functions as a function on products.
• Define the uniform continuity for f:X->Y: for any entourage V in Y; (fxf)-``(V) is an entourage in X
• Show that they are continous for the associated topologies
• Give an example of continuous non uniformly continuous map