  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 H\"older regularity lies between 0.35 and 0.72 almost
everywhere (with respect to the Lebesgue measure).

Functional Analysis;Classical Analysis and ODEs