English

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

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