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On superpositions of continuous functions defined on the baire space

Authors
  • Marchenkov, S. S.1
  • 1 Russian Academy of Sciences, M. V. Keldysh Institute of Applied Mathematics, USSR
Type
Published Article
Journal
Mathematical Notes
Publisher
Kluwer Academic Publishers-Plenum Publishers
Publication Date
Nov 01, 1999
Volume
66
Issue
5
Pages
577–584
Identifiers
DOI: 10.1007/BF02674199
Source
Springer Nature
Keywords
License
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Abstract

For continuous functions specified on the Baire space, conditions for the representability of a function of several variables as a superposition of functions of a smaller number of variables are considered. With the use of linear functions of the form (1+α)t, a boundary value of the modulus of continuity separating the positive from the negative solution of the problem is found. For the case in which the problem has a negative solution, a constructive method for obtaining (n+1)-variable continuous functions with modulus of continuity ϕ(t) that are not representable as superposition ofn-variable continuous functions with the same modulus of continuity ϕ(t) is suggested.

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