On the geometry of an order unit space

Abstract

We introduce the notion of skeleton with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which V contains a copy of \(\ell _{\infty }^n\) for some \(n \in {\mathbb {N}}\) as an order unit subspace.