Let $C$ and $D$ be two non-empty convex subsets of $\mathbb{R}^d$ such that $C$ is closed and bounded, $D$ is closed, and $C \cap D = \emptyset$. Show that $D - C$ is a convex closed subset of $\mathbb{R}^d$ not containing $0$.
Let $C$ and $D$ be two non-empty convex subsets of $\mathbb{R}^d$ such that $C$ is closed and bounded, $D$ is closed, and $C \cap D = \emptyset$. Show that $D - C$ is a convex closed subset of $\mathbb{R}^d$ not containing $0$.