It is mentioned that we can only separate two convex sets only when at least one is bounded (compact). Now if we take epigraph of $f(x) = x^2 +1$ and the other is below the $x$ axis, I can find a function $f(x)=0.5$ that can separate these two epigraphs which are convex and unbounded. Please help me to understand where I am wrong in my understanding?
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That's only sufficient condition for strong separation not necessary. So of course there are many convex unbound sets which have positive distance – Red shoes Jul 13 '17 at 11:22
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Thanks for explanation. – Arun Chauhan Jul 14 '17 at 12:59