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.
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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. |
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