On the polynomiality of separately constant functions

  • 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
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.
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