On fractal Peano curves
Metric Geometry
2007-05-23 v1 Geometric Topology
Abstract
It 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|.
Keywords
Cite
@article{arxiv.math/0404533,
title = {On fractal Peano curves},
author = {Evgeny Shchepin},
journal= {arXiv preprint arXiv:math/0404533},
year = {2007}
}
Comments
11 pages, in Russian, to appear in Proc. Steklov Math. Inst