manuscripta mathematica

, Volume 27, Issue 3, pp 291–312 | Cite as

Fortsetzungen von C-Funktionen, welche auf einer abgeschlossenen Menge in ℝn definiert sind

  • Michael Tidten
Article

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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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Michael Tidten
    • 1
  1. 1.Fachbereich Mathematik der Gesamthochschule WuppertalWuppertal 1Bundesrepublik Deutschland

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