Real Algebraic and Analytic Geometry

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61. Wiesław Pawłucki:
On the algebra of functions Ck-extendable for each k finite.


Submission: 2003, October 9.

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

Mathematics Subject Classification (2000): 26E10, 32S05, 32B20.

Full text, 4p.: dvi 16k, ps.gz 116k, pdf 153k.

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