A central set of dimension 2

Bishop, Christopher; Hakobyan, Hrant

doi:10.1090/S0002-9939-08-09173-9

A central set of dimension $2$
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by Christopher J. Bishop and Hrant Hakobyan PDF

Proc. Amer. Math. Soc. 136 (2008), 2453-2461 Request permission

Abstract:

The central set of a domain $D$ is the set of centers of maximal discs in $D$. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than $1$. We construct a planar domain with central set of Hausdorff dimension $2$.

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