Geodesic
On superpositions of continuous functions
Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 517-522 
A. A. Agrachev. On superpositions of continuous functions. Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 517-522. http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a1/
@article{MZM_1974_16_4_a1,
     author = {A. A. Agrachev},
     title = {On superpositions of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--522},
     year = {1974},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a1/}
}
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%J Matematičeskie zametki
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\psi(x_1,\dots,x_n)$ such that $\psi(x_1,\dots,x_n)\not\equiv g[\varphi(f_1(x_1),\dots,f_n(x_n))]$ for any function $\varphi$ from $\Phi$ and arbitrary continuous functions $g$ and $f_i$, depending on a single variable.