Supporting hyperplane theorem
= Supporting hyperplane theorem
{wiki}
A <convex set> in a finite-dimensional space has a nonzero supporting linear functional at each boundary point. If zero lies outside a nonempty <convex set> $C$, weak separation gives $p\ne0$ with $p\cdot c\geq0$ for all $c\in C$, even when zero belongs to its closure. Strict separation needs stronger hypotheses.