A Closed Convex Set is the Intersection of all Closed Halfspaces containing it

Last updated Nov 1, 2022

Let $V$ be an Inner Product Space over $\mathbb{R}$ and $S \subset V$ be Closed and convex. Then $$S = \bigcap\limits_{} {H \subset V : S \subset H, H \text{ is a closed halfspace}}$$

TODO - see Boyd - Convex Optimization section 2.5 pg 46