Question: Let S be a nonempty, closed, convex set in a Euclidean space X and y S. There exists a continuous linear functional f

Let S be a nonempty, closed, convex set in a Euclidean space X and y ∉ S. There exists a continuous linear functional f ∈ X* and a number c such that
f (y) < c ≤ f (x) for every x ∈ S

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