Separation of a finite set in \(\mathbb{R}^ d\) by spanned hyperplanes
Let \(k\) be any natural number. The author shows that each subset \(V\) of Euclidean 3-space \(E^ 3\) (which spans \(E^ 3\) affinely) with at least \(4k+1\) points possesses some subset spanning a plane \(J\) such that each open half-space determined by \(J\) contains at least \(k\) points of \(V\).
scientific article; zbMATH DE number 484130