A simpler proof of the Sternfeld theorem

Abstract

In Sternfeld's work on Kolmogorov Superposition Theorem appeared combinatorialgeometric notions of a basic set and of a Sternfeld's array.A subsetThe notion of a Sternfeld's array will be introduced in the paper.Sternfeld Theorem. If a closed bounded subset K ⊂ R 2n contains Sternfeld arrays of arbitrary large size then K is not basic.