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Example of a function of two variables that cannot be an R-function

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We note that the definition of R-functions depends on the choice of a certain surjection and pose the problem of the construction of a function of two variables that is not an R-function for any choice of a surjective mapping. It is shown that the function x 1 x 2 − 1 possesses this property. We prove a theorem according to which, in the case of finite sets, every mapping is an R-mapping for a proper choice of a surjection.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 270–274, February, 2010.

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Velichko, I.G., Stegantseva, P.G. Example of a function of two variables that cannot be an R-function. Ukr Math J 62, 308–313 (2010). https://doi.org/10.1007/s11253-010-0353-3

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  • DOI: https://doi.org/10.1007/s11253-010-0353-3

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