On the algebra of functions <IMG BORDER="0" SRC="http://www.ams.org/proc/2005-133-02/S0002-9939-04-07756-1/gif-title0/img1.gif" >-extendable for each <IMG BORDER="0" SRC="http://www.ams.org/proc/2005-133-02/S0002-9939-04-07756-1/gif-title0/img2.gif" > finite期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the algebra of functions -extendable for each finite

Authors:	Wieslaw Pawlucki

Institution:	Instytut Matematyki, Uniwersytetu Jagiellonskiego, ul. Reymonta 4, 30-059 Kraków, Poland

Abstract:	For each positive integer we construct a $\mathcal C^l$ -function of one real variable, the graph $\Gamma$ of which has the following property: there exists a real function on $\Gamma$ which is $\mathcal C^k$ -extendable to $\mathbb{R} ^2$ , for each finite, but it is not $\mathcal C^{\infty}$ -extendable.

Keywords:	$\mathcal C^k$-function extension Whitney field

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