A simpler proof of Sternfeld's Theorem

In Sternfeld's work on Kolmogorov's Superposition Theorem appeared the combinatorial-geometric notion of a basic set and a certain kind of arrays. A subset X subset of R-n is basic if any continuous function X -> R could be represented as the sum of compositions of continuous functions R -> R and projections to the coordinate axes. The definition of a Sternfeld array will be presented in the paper. Sternfeld's Arrays Theorem. If a closed bounded subset X subset of R-2n contains Sternfeld arrays of arbitrary large size then X is not basic. The paper provides a simpler proof of this theorem.