Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.
|
|
|
Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Separation Hyperplane Theorem
Replies:
2
Last Post:
Oct 12, 2012 3:20 PM
|
 |
|
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
|
|
|
|
