## Describing a set of normals

In a finite dimensional (think Euclidean) ambient space, let $S$ a compact, convex set and $x$ not in $S$. The two sets can be (weakly) separated, i.e. there exists a vector (normal) that defines a hyperplane separating the point and the set. In fact, there exists an entire (open) set of normals that separate the point and the set. How can one describe this set?

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 See math.stackexchange.com/questions/17143/… – Theo Buehler Jan 12 2011 at 1:32