JournalszaaVol. 19, No. 3pp. 847–852

On the Existence of C1C^1 Functions with Perfect Level Sets

  • Emma D'Aniello

    Università degli Studi di Napoli, Caserta, Italy
  • U.B. Darji

    University of Louisville, USA
On the Existence of $C^1$ Functions with Perfect Level Sets cover
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Abstract

Given a closed set M[0,1]M \subset [0, 1] of Lebesgue measure zero, we construct a C1C^1 function ff with the property that f1(y)f^{–1} ({y}) is a perfect set for every yy in MM.

Cite this article

Emma D'Aniello, U.B. Darji, On the Existence of C1C^1 Functions with Perfect Level Sets. Z. Anal. Anwend. 19 (2000), no. 3, pp. 847–852

DOI 10.4171/ZAA/983