| Abstract: | For continuous functions specified on the Baire space, conditions for the representability of a function of several variables
as a superposition of functions of a smaller number of variables are considered. With the use of linear functions of the form
(1+α)t, a boundary value of the modulus of continuity separating the positive from the negative solution of the problem is found.
For the case in which the problem has a negative solution, a constructive method for obtaining (n+1)-variable continuous functions with modulus of continuity ϕ(t) that are not representable as superposition ofn-variable continuous functions with the same modulus of continuity ϕ(t) is suggested.
Translated fromMatermaticheskie Zametki, Vol. 66, No. 5, pp. 696–705, November, 1999. |
