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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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    Perhaps this will help http://en.wikipedia.org/wiki/Separating_axis_theorem2011-01-12
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    @Trevor: thank you. It seems to me that it is a re-iteration of the question on the "primal" space.2011-01-12

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