Re: Example of a set requiring d+1 points (Caratheodory theorem)

On Fri, 22 Feb 2008 15:42:28 -0800 (PST), Dash <ddash.res@xxxxxxxxx>
wrote:

Hi,
I have a trivial doubt about a form of Caratheodory theorem which has
applications in Information Theory. The statement of the theorem is,
"Any point in the convex closure of a connected compact set A in a d
dimension Euclidean space can be represented as a convex combination
of d+1 or fewer points in the original set A."

My problem is that I am unable to find any example where d+1 points
are required. (It is easy to find examples where only d points
suffice). In addition, is there an example in R^n?

Any help will be greatly appreciated.

A triangular region in R^2.

Or for that matter, a closed interval in R^1.

quasi
.

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