A central set of dimension $2$
Christopher J. Bishop, Hrant Hakobyan · Proceedings of the American Mathematical Society · 2008
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 $2$.