On the polynomiality of separately constant functions

V. M. Kosovan, V. K. Maslyuchenko


We establish necessary conditions and sufficient conditions on a set $E\subseteq  \mathbb{R}^2$ under which every separately constant function $f:E\to \mathbb{R}$ is polynomial and there exist a separately constant function $f_0:E \to \mathbb{R}$ which is not constant.


polynomiality, separately constant function

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