On the polynomiality of separately constant functions - Kosovan, V.M.; Maslyuchenko, V.K. (Carpathian Mathematical Publications, 2014)
We establish necessary conditions and sufficient conditions on a set $E\subseteq \mathbb{R}^2$ under which every separately constant function $f:E→ \mathbb{R}$ is polynomial and there exist a separately constant function $f_0:E → \mathbb{R}$ which is not constant.