Real Algebraic and Analytic Geometry |

On the algebra of functions

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Submission: 2003, October 9.

*Abstract:
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.

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