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Maury Barbato
Posts:
792
From:
University Federico II of Naples
Registered:
3/15/05


Separation Hyperplane Theorem
Posted:
Oct 12, 2012 2:22 PM


Hi, let A and B two disjoint closed convex subsets of R^n. Then the standard separation hyperplane theorem states that there exists some linear functional such that L(x) <= L(y) for every x in A and y in B. I think that actually a stronger result holds, that is there exists a linear functional L such that L(x) < L(y) for every x in A and y in B. What do you think about? Note that I have supposed that A and B are closed. Thank you very much in advance for your attention. My Best Regards, Maury Barbato



