Example of a function of two variables that cannot be an R-function - Velichko, I. G.; Stegantseva, P. G. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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.