Geodesic
Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators
Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 863-878

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Continuous functions on a unit cube are considered. The concept of continuity regulator is introduced: in the definition of uniform continuity it governs the transition "from $\varepsilon$ to $\delta$". The problem of obtaining continuous functions of $(n+1)$ variables with continuity regulator $\delta$ variables with the same continuity regulator by means of uniformly continuous operators with continuity regulators that are superpositions of the regulator $\delta$ is posed. The insolubility of this problem is demonstrated for continuity regulators $\delta$ ($\varepsilon$) such that for each $\alpha\geqslant0$ the inequality $\delta(\varepsilon)\geqslant\varepsilon^{1+\alpha}$ holds starting from some $\varepsilon_\alpha$. 
@article{SM_2001_192_6_a4,
     author = {S. S. Marchenkov},
     title = {Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators},
     journal = {Sbornik. Mathematics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_6_a4/}
}
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S. S. Marchenkov. Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators. Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 863-878. http://geodesic.mathdoc.fr/item/SM_2001_192_6_a4/