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 on derivatives
Department of Mathematics, Portland State University, Portland 97207, Oregon, USA
Received 7 March 1985
Copyright © 1986 F. S. Cater. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.