If $C \subseteq E$ is a closed convex set define $$C^{\circ}=\bigcap_{x\in C}\{u \in E: \langle u,x\rangle\leq 1\}$$ Determine $C^{o}$ if $C= \{x: Ax \leq b\}$
Solution so far:
$C^{o}=\bigcap_{x\in C}\{u \in E: \langle u,x\rangle\leq 1\}=\{u \in E: \langle u,x\rangle\leq 1 \> \forall x \in C\}=\{u \in E: \langle u,x\rangle\leq 1 \>with\> Ax\leq b\}$