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On fractal Peano curves

Evgeny Shchepin
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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|.

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Evgeny Shchepin. 2004-04-29. On fractal Peano curves. https://arxiv.org/abs/math/0404533

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