Dimension of metric spaces and Hilbert’s problem 13

In 1957 A. N. Kolmogorov [l] and V. I. Arnol'd [2] obtained the following result (answering Hubert's conjecture in the negative) : THEOREM.For every integer n*z2 there exist continuous real f unctions $ pq ,for p = l, 2, • • • , n and q = l, 2, • • • , 2w+l, defined on the unit interval E 1 = [0, 1 ], such that every continuous real function f, defined on the n-dimensional unit cube E n , is representable in the form 2n+l r-n "I «=-i L p-i J