Smooth images of the irrationals. (English) Zbl 1128.26002

D’Aniello, Emma; Darji, Udayan B.

Real Anal. Exch. 32(2006-2007), No. 1, 19-28 (2007).

The authors study descriptive set-theoretic as well as measure-theoretic properties of smooth images of the irrationals. They state some results concerning smooth images of the irrationals where smoothness is in terms of Peano derivatives. These results bring them closer to a solution of the “parametrization” problem.

Reviewer: Mourad Ben Slimane (Tunis)

MSC:

26A30	Singular functions, Cantor functions, functions with other special properties
26A16	Lipschitz (Hölder) classes

Keywords:

analytic sets; Lipschitz maps; Hausdorff dimension