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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Separation Hyperplane Theorem
Replies: 2   Last Post: Oct 12, 2012 3:20 PM

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Maury Barbato

Posts: 789
From: University Federico II of Naples
Registered: 3/15/05
Separation Hyperplane Theorem
Posted: Oct 12, 2012 2:22 PM
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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

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