On the Existence of $C^1$ Functions with Perfect Level Sets

Emma D'Aniello; U.B. Darji

doi:10.4171/zaa/983

JournalszaaVol. 19, No. 3pp. 847–852

On the Existence of $C^{1}$ Functions with Perfect Level Sets

Emma D'Aniello
Università degli Studi di Napoli, Caserta, Italy
U.B. Darji
University of Louisville, USA

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Abstract

Given a closed set $M \subset [0, 1]$ of Lebesgue measure zero, we construct a $C^{1}$ function $f$ with the property that $f^{-1} (y)$ is a perfect set for every $y$ in $M$ .

Cite this article

Emma D'Aniello, U.B. Darji, On the Existence of $C^{1}$ Functions with Perfect Level Sets. Z. Anal. Anwend. 19 (2000), no. 3, pp. 847–852

DOI 10.4171/ZAA/983