Derivatives and closed sets

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1984 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 43, pages 25-29 (issn: 0236-5294, eissn: 1588-2632,

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Authors: Mařík, J.;

doi: 10.1007/bf01951320

Derivatives and closed sets

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Abstract

The author proves that a real function defined on a closed set S and differentiable relative to S can be extended to a function differentiable on the whole real line. This is a generalization of a result of \textit{G. Petruska} and \textit{M. Laczkovich} [Acta. Math. Acad. Sci. Hung. 25, 189- 212 (1974; Zbl 0279.26003)].

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Michigan State University
United States

Keywords

extension to a function differentiable on the whole real line, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, closed set

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