Iteration operators on a set of continuous functions of Baire space

Abstract

Continuous functions on Baire space are considered. Iteration operators are defined on a set of continuous functions. The idea of a module of continuity of a function is introduced. The condition for the growth of module of continuity φ whose satisfaction guarantees that for any enumerable sequence of integration operators and any natural n there exists (n + 1) argument function with the module of continuity φ which cannot be obtained from n-argument functions with the module of continuity φ using any operator of this sequence is formulated. Examples of iteration operators are given.