arXiv subjects

Laurent Simons

Publications and source records attributed to Laurent Simons.

2 recordsLinked to original sources

arXiv2014

Building Cantor's Bijection

Cantor's first idea to build a one-to-one mapping from the unit interval to the unit square did not work since, as pointed out by Dedekind, the so-obtained function is not surjective. Here, we start from this function and modify it (on a negligible set) in order to obtain the desired result: a one-to-one correspondance between the unit interval and the unit square.

math.HO↗

arXiv2014

About the multifractal nature of Cantor's bijection

In this note, we investigate the regularity of Cantor's one-to-one mapping between the irrational numbers of the unit interval and the irrational numbers of the unit square. In particular, we explore the fractal nature of this map by showing that its Hölder regularity lies between 0.35 and 0.72 almost everywhere (with respect to the Lebesgue measure).

math.FA↗