Does one always exist? I see that it is true in finite dimensions.
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Do you know the geometrical form of Hahn Banach theorem? – mathcounterexamples.net Jan 02 '16 at 17:58
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Yes. I am not assuming that the set has interior. – Rick Jan 02 '16 at 18:19
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What about considering the linear span of the convex which has an interior? – mathcounterexamples.net Jan 02 '16 at 18:22
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Did you mean "linear span of the convex hull"? Not sure I understand your idea. – Rick Jan 02 '16 at 19:09
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I mean linear span of your initial convex set. – mathcounterexamples.net Jan 02 '16 at 20:14