A simultaneous solution to two problems on derivatives

F. S. Cater

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-3

Abstract:

Let A be a nonvoid countable subset of the unit interval [ 0 , 1 ] and let B be an F σ -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.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:745496

DOI: 10.1155/S0161171286000637

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