Question: Generalize exercise 3.182 to dispense with the assumption that S is closed. That is, let S be a nonempty, convex set in a Euclidean space

Generalize exercise 3.182 to dispense with the assumption that S is closed. That is, let S be a nonempty, convex set in a Euclidean space X and y ∉ S.
There exists a continuous linear functional f ∈ X* such that
f (y) ≤ f (x). for every x ∈ S

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