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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

Information

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 

References

1.Engelking, R., General topology, revised edn (Heldermann, Berlin, 1989).Google Scholar
2.Falconer, K., Fractal geometry: mathematical foundations and applications, 2nd edn (Wiley, 2003).Google Scholar
3.Gromov, M., Partial differential relations (Springer, 1986).Google Scholar
4.Mattila, P., Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, Volume 44 (Cambridge University Press, 1995).Google Scholar