On the polynomiality of separately constant functions

V.M. Kosovan; V.K. Maslyuchenko

doi:10.15330/cmp.6.1.59-63

On the polynomiality of separately constant functions

Authors

V.M. Kosovan Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
V.K. Maslyuchenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine

https://doi.org/10.15330/cmp.6.1.59-63

Keywords:

polynomiality, separately constant function

Published online: 2014-07-14

Abstract

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.