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Sbornik: Mathematics, 2001, Volume 192, Issue 6, Pages 863–878
DOI: https://doi.org/10.1070/SM2001v192n06ABEH000573
(Mi sm573)
 

This article is cited in 3 scientific papers (total in 3 papers)

Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators

S. S. Marchenkov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
References:
Abstract: 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 $\varepsilon_\alpha$.
Received: 24.08.2000
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 6, Pages 71–88
DOI: https://doi.org/10.4213/sm573
Bibliographic databases:
UDC: 519.716
MSC: Primary 26B40, 26B35; Secondary 41A63, 41A30
Language: English
Original paper language: Russian
Citation: S. S. Marchenkov, “Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators”, Mat. Sb., 192:6 (2001), 71–88; Sb. Math., 192:6 (2001), 863–878
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v192/i6/p71
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Russian version PDF:203
    English version PDF:21
    References:57
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