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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Translated fromMatermaticheskie Zametki, Vol. 66, No. 5, pp. 696–705, November, 1999.
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Marchenkov, S.S. On superpositions of continuous functions defined on the baire space. Math Notes 66, 577–584 (1999). https://doi.org/10.1007/BF02674199
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DOI: https://doi.org/10.1007/BF02674199