Upper hemicontinuity
= Upper hemicontinuity
= Upper hemicontinuous
{synonym}
A <set-valued mapping> $F$ is upper hemicontinuous at $x$ when every open set containing $F(x)$ also contains $F(x')$ for all nearby $x'$. With values in a fixed <compact> space, a closed <graph of a set-valued mapping> implies <upper hemicontinuity>: a violating sequence has a convergent subsequence of outputs whose limit lies in the limiting value.