am working on a proof to present to a reading group I am in, that relies on the following proposition, which I am having trouble proving. Perhaps some of the brilliant minds that frequent this forum may find an opportunity to help.

Suppose that M(x) is an USC correspondence from S-->T, S in Rm, T compact in Rn.

I want to claim that for every x(n)-->x, there exists a sequence

y(n):y(n) is an element of M(x(n)), which converges.

Since T is compact, for ANY sequence y(n) st y(n) in M(x(n)), there exists a SUBsequence which converges, but I need an element y(n) in
M(x(n)) for EVERY x(n).

In case the reader is wondering, I am trying to prove that if f is continuous and M is usc, then the correspondence f(x,M(x)) is also usc, which in turn I am using to prove the Berge "theorem of the maximum." Any ideas would be much appreciated