International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 517-519

A simultaneous solution to two problems on derivatives

F. S. Cater

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.


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 0f1, f=0 on A, f>0 on B, and such that the extended real valued function 1/f is also a derivative.