On an old theorem of Erd
Piotr Hajłasz · Colloquium Mathematicum · 2022
Erdős proved in 1946 that if a set $E\subset \mathbb R ^n$ is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in $\mathbb R ^n$ with the property that the nearest point in $E$ is not unique, can be covered by countably