Separating [formula omitted]-point sets from quasi-finite ones via polyhedral surfaces

Abstract

Let X be an infinite set in Rd that has no accumulation point. We prove that the following statement holds for each d-dimensional polyhedron Π, i.e., for each bounded part of Rd generated by a closed polyhedral surface: for any positive integer n, there is a polyhedron similar to Π that contains exactly n points taken from X.