Hemicontinuity
= Hemicontinuity
= Hemicontinuous
{synonym}
For a real <Banach space> $X$ and a <convex set> $K\subset X$, a map $A:K\to X^*$ is <hemicontinuous> if $t\mapsto\langle A(x+t(y-x)),z\rangle$ is continuous on $[0,1]$ for all $x,y\in K$ and $z\in X$. This tests <continuity> only along <line segments> and only through pairings with fixed <vectors>. It is enough for the limiting step in <Minty's lemma>.