Abstract
In this paper the problem is considered of finding linear, continuous extension operators which extend Whitney-functions of type C∞ on a closed set in ℝn to C∞-functions on the whole space. It is shown that a sort of horn condition for the closed set A is sufficient for the existence of an extension operator on ξ(A). The methods are different from Bierstone's [2] who recently proved the same extension result for closed sets A for instance whose boundary ∂A is locally the graph of a function of Lipschitz class ℒ. A further result is an equivalent description for the existence of an extension operator by the topology of ξ(K) in the case of a compact set K. From this there are derived some examples of compact sets which are the closures of their interiors such that there exists no extension operator.
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Tidten, M. Fortsetzungen von C∞-Funktionen, welche auf einer abgeschlossenen Menge in ℝn definiert sind. Manuscripta Math 27, 291–312 (1979). https://doi.org/10.1007/BF01309013
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DOI: https://doi.org/10.1007/BF01309013