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

• Date: 2010
• Main Authors: Velichko, I. G., Stegantseva, P. G., Величко, И. Г., Стеганцева, П. Г.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2863
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 p...