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Intersection of Continua and Rectifiable Curves

Published online by Cambridge University Press:  21 August 2013

Richárd Balka  and
Viktor Harangi
Richárd Balka
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary, (balka.richard@renyi.mta.hu; harangi.viktor@renyi.mta.hu)
Viktor Harangi
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary, (balka.richard@renyi.mta.hu; harangi.viktor@renyi.mta.hu)
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Abstract

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We prove that for any non-degenerate continuum K ⊆ ℝd there exists a rectifiable curve such that its intersection with K has Hausdorff dimension 1. This answers a question of Kirchheim.

Keywords

continuumrectifiable curveHausdorff dimensionPrimary 28A78
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 339 - 345
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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