On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy
| Autor: | John L. Leonard, A. M. Bruckner |
|---|---|
| Rok vydání: | 1965 |
| Předmět: |
Dense set
General Mathematics 010102 general mathematics 010103 numerical & computational mathematics Function (mathematics) Cantor function Absolute continuity Topology 01 natural sciences Combinatorics Cantor set symbols.namesake symbols Interval (graph theory) Differentiable function 0101 mathematics Constant (mathematics) Mathematics |
| Zdroj: | Canadian Mathematical Bulletin. 8:73-76 |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/cmb-1965-009-1 |
| Popis: | The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties:(i)C is defined on [0,1], with C(0) = 0, C (l) = l;(ii)C is continuous and non-decreasing on [0,1];(iii)C is constant on each interval contiguous to the perfect Cantor set P;(iv)C fails to be constant on any open interval containing points of P;(v)The set of points at which C is non-differentiable is non-denumerable. |
| Databáze: | OpenAIRE |
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