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Superpositions of continuous functions defined on a Baire space

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Abstract

We consider uniformly continuous functions on a Baire space and introduce the notion of a continuity modulus of a function. We formulate a condition on the growth of the continuity modulus φ guaranteeing that superpositions of n-ary functions with continuity modulus φ do not exhaust all (n + 1)-ary functions with continuity modulus φ for any n. Moreover, negating this property leads to the inverse effect.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    S. S. Marchenkov & S. I. Krivospitsky

Authors
  1. S. S. Marchenkov
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  2. S. I. Krivospitsky
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Correspondence to S. S. Marchenkov.

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Original Russian Text © S.S. Marchenkov, S.I. Krivospitsky, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 4, pp. 107–114.

Supported in part by the Russian Foundation for Basic Research, project no. 09-01-00701.

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Marchenkov, S.S., Krivospitsky, S.I. Superpositions of continuous functions defined on a Baire space. Probl Inf Transm 45, 393–399 (2009). https://doi.org/10.1134/S0032946009040085

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