On separately polynomial functions
type: Item
instance of: scholarly article
title: On separately polynomial functions
zbMATH Open document ID: 0729.26013
DOI: 10.1007/BF01199018
author: Zoltán Sasvári
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: In a recent issue of Am. Math. Mon. [Vol. 97, No.7 (1990)] \textit{J. Totaro} proposed the following problem: Let S be the boundary of the unit square [0,1]\(\times [0,1]\) in \({\mathbb{R}}^ 2\). Suppose f is a continuous real-valued function on S such that f(x,0) and f(x,1) are polynomial functions of x on [0,1] and such that f(0,y) and f(1,y) are polynomial functions of y on [0,1]. Prove that f is the restriction of a polynomial function of x and y. It is the aim of the present note to generalize this problem and then to give a new proof of a result of R. S. Palais on separately polynomial functions.
Mathematics Subject Classification ID: 26C05
Mathematics Subject Classification ID: 26B05
zbMATH DE Number: 4204708
zbMATH Keywords: boundary
zbMATH Keywords: unit square
zbMATH Keywords: separately polynomial functions
MaRDI profile type: Publication
cites work: Some Analogues of Hartogs' Theorem in an Algebraic Setting
full work available at URL: https://doi.org/10.1007/bf01199018
OpenAlex ID: W131700369
description: scientific article; zbMATH DE number 4204708