2004/04/29 by Evgeny Shchepin, Shchepin, Evgeny
Mathematics · #28A80 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG #msc:28A80
paper · pdf · doi:10.48550/arxiv.math/0404533
11 pages, in Russian, to appear in Proc. Steklov Math. Inst
arxiv created 2004/04/29 · arxiv updated 2009/12/01
It is proved that for every fractal continuous mapping F: I→ I2 of the unit interval onto the unit square there is a pair of points x,y∈ I, such that |F(x)-F(y)|2≥ 5|x-y|.