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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the algebra of functions $\mathcal{C}^k$-extendable for each $k$ finite


Author: Wieslaw Pawlucki
Journal: Proc. Amer. Math. Soc. 133 (2005), 481-484
MSC (2000): Primary 26E10; Secondary 32S05, 32B20
Published electronically: September 8, 2004
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Abstract: For each positive integer $l$ 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 $k$ finite, but it is not $\mathcal C^{\infty}$-extendable.


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Additional Information

Wieslaw Pawlucki
Affiliation: Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Reymonta 4, 30-059 Kraków, Poland
Email: Wieslaw.Pawlucki@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07756-1
PII: S 0002-9939(04)07756-1
Keywords: $\mathcal C^k$-function, extension, Whitney field
Received by editor(s): October 13, 2003
Published electronically: September 8, 2004
Additional Notes: This research was partially supported by the KBN grant 5 PO3A 005 21 and the European Community IHP-Network RAAG (HPRN-CT-2001-00271)
Communicated by: David Preiss
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.