Suppose that fi:Ai -> Bi is an upper hemicontinuous correspondence for 1 i n.
Define F:A1A2...An -> B1B2...Bn to be a correspondence such that, for all a=(a1,a2,...,an) belonging to A1A2...An, F(a):= f1(a1)f2(a2)...fn(an).
How do I show that F is also upper hemicontinuous?

Here,
definition 1:
A correspondence F: X-> Y is a map F from X to "subsets of Y".
definition 2:
A correspondence F: X-> Y is upper hemicontinuous if, for each sequence {xk} X converging to x' belonging to X and each open set Y* Y such that F(x') Y*, there is a natural number k0 such that, for each k k0, F(xk) Y*.