Theorems on the existence of separating surfaces (Q756705)

Let R and G be finite sets in \(E^ d\). Kirchberger's theorem implies that the strict linear separability of R and G is determined by the separability of all subsets of up to \(d+2\) points of \(R\cup G\). This paper shows that under certain conditions, the linear separability of R and G is determined by the separability of significantly fewer than all subfamilies of up to \(d+2\) members of R and G. The same treatment is made of Lay's extension of Kirchberger's theorem to separation by hyperspheres.