Doubling metric spaces, which are studied a lot, have this property. A metric space is doubling provide provided there exists $n$ so that for every $r>0$, a ball of radius $2r$ is covered by $n$ balls of radius $r$. Google "doubling metric spaces"; some of the half million hits should be useful.
Doubling metric spaces, which are studied a lot, have this property. A metric space is doubling provide there exists $n$ so that for every $r>0$, a ball of radius $2r$ is covered by $n$ balls of radius $r$. Google "doubling metric spaces"; some of the half million hits should be useful.