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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 517-519
doi:10.1155/S0161171286000637

A simultaneous solution to two problems of derivatives

F.S. Cater

Department of Mathematics, Portland State University, Portland 97207, Oregon, USA

Abstract

Let A be a nonvoid countable subset of the unit interval [0,1] and let B be an Fσ-subset of [0,1] disjoint from A. Then there exists a derivative f on [0,1] such that 0≤f≤1, f=0 on A, f>0 on B, and such that the extended real valued function 1/f is also a derivative.