Impossibility of constructing continuous functions of n+1 variables from functions of n variables by means of certain continuous operators

Continuous functions on a unit cube are considered. The concept of continuity regulator is introduced: in the definition of uniform continuity it governs the transition 'from epsilon to delta'. The problem of obtaining continuous functions of n + 1 variables with continuity regulator delta from functions of n variables; with the same continuity regulator by means of uniformly continuous operators with continuity regulators that are superpositions of the regulator delta is posed. The insolubility of this problem is demonstrated for continuity regulators delta(epsilon) such that for each alpha greater than or equal to 0 the inequality delta(epsilon) greater than or equal to epsilon (1+alpha) holds starting from some epsilon (alpha).