Re: hahn banach

In article <1142425130.210729.3670@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Fedor <malabar_carotte@xxxxxxxxx> wrote:
hi all,

I'm searching an example of two convex sets A and B that cannot be
separated by an hyperplane. I think they exist but I can't find simple
examples ..

I am presuming you mean disjoint convex sets. The
"classical" is the space of all polynomials over the
reals, where A is the set of all polynomials whose
leading coefficient is positive, and b the set whose
leading coefficient is negative.

To avoid this problem in infinite dimensional spaces,
one needs to assume that one of the sets has an
internal point. This is a point such that any line
through the point has an open interval containing the
point which lies entirely in the set.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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