Abstract:A real function $f$ on $[0,\;1]$ can be transformed by a homeomorphism into a differentiable function with bounded derivative if and only if $f$ is continuous and of bounded variation. This condition does not suffice for $f$ to be transformed into a continuously differentiable function. The additional condition for this to hold is found and the theorem is proved.
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- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 235-241
- MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-1976-0432831-2
- MathSciNet review: 0432831