Title: On superpositions of continuous functions

Authors: A.A. Agrachev

Journal title: Mathematical Notes

Year: 1974

Issue: 4

Volume: 16

Pages: 897–900

Citation:

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

Abstract:

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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MathNet (ENG): http://mi.mathnet.ru/eng/mz7489