A continuous function not twice Peano differentiable on any perfect set (Q1374570)
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scientific article; zbMATH DE number 1095877
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A continuous function not twice Peano differentiable on any perfect set |
scientific article; zbMATH DE number 1095877 |
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A continuous function not twice Peano differentiable on any perfect set (English)
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10 December 1997
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\textit{M. Laczkovich} [Acta Math. Hung. 44, 355-360 (1984; Zbl 0558.26005)] proved that for every continuous, real valued function of one real variable there is a nonempty, perfect set with respect to which the function is infinitely differentiable. In the paper is given an example of a continuous function that is differentiable except on a countable set, but is not twice Peano differentiable on any nonempty, perfect set.
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Peano differentiable function
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perfect set
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