2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71008It is proved that for every fractal continuous mapping F: I\to I^2 of the unit interval onto the unit square there is a pair of points x,y\in I, such that |F(x)-F(y)|^2\ge 5|x-y|.11 pages, in Russian, to appear in Proc. Steklov Math. InstMetric GeometryGeometric Topology28A80text