On Lipschitz Mappings Onto a Square

Jiří Matoušek ()
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Jiří Matoušek: Charles University, Department of Applied Mathematics, Institute of Theoretical Computer Science (ITI)

A chapter in The Mathematics of Paul Erdős I, 2013, pp 533-540 from Springer

Abstract: Abstract The following problem was posed by Laczkovich [5]: Let $$E \subseteq \mathbb{R}{\mathbb{R}}^{d}$$ (d ≥ 2) be a set with positive Lebesgue measure λ d (E) > 0. Does there exist a Lipschitz mapping $$f : {\mathbb{R}}^{d} \rightarrow Q = {[0,1]}^{d}$$ , such that f(E) = Q? Preiss [6] answered this question affirmatively for d = 2:

Keywords: Mapping Onto; Laczkovich; Positive Lebesgue Measure; Axis-parallel Square; Usual Euclidean Metric (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_33

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DOI: 10.1007/978-1-4614-7258-2_33

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