A.A. Agrachev, On superpositions of continuous functions

Title: On superpositions of continuous functions
Authors: A.A. Agrachev
Journal title: Mathematical Notes
Year: 1974
Issue: 4
Volume: 16
Pages: 897–900

A. A. Agrachev, “On superpositions of continuous functions”, Mat. Zametki, 16:4 (1974), 517–522


We show that if \Phi is an arbitrary countable set of continuous functions of n variables, then there exists a continuous, and even infinitely smooth, function \psi(x_1, ..., x_n) such that \psi(x_1, ..., x_n) \neq g [\phi (f_1(x_1), ..., f_n(x_n)] for any function \phi from \Phi and arbitrary continuous functions g and f_i depending on a single variable.

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