On fractal Peano curves

Details On fractal Peano curves On fractal Peano curves

2004-04-29

arxiv.org/abs/math/0404533v1

Mathematics

Metric Geometry

11 pages, in Russian, to appear in Proc. Steklov Math. Inst

Scientific paper

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|.

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