2
$\begingroup$

Let $W$ be a set of points in $\mathbb{R}^n$. Let $C$ be the convex hull of the members of $W$. Is there a simple way of demonstrating that for any $x \in C$ and any $y \in \mathbb{R}^n \backslash C$, there must be some $w \in W$ such that $\|w - x\| < \|w - y\|$?

2 Answers 2