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Proceedings of the Edinburgh Mathematical Society (1)

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Intersection of Continua and Rectifiable Curves
Richárd Balka, Viktor Harangi
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Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 2 / June 2014

Published online by Cambridge University Press:

21 August 2013, pp. 339-345
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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.