Metric space/Distance/Subsets/Infimum/Definition

Distance of subsets

For two nonempty subsets ${}A,B\subseteq M$ in a metric space ${}M$,

${}d(A,B):=\inf {\left(d(P,Q),\,P\in A,\,Q\in B\right)}\,$

is called the distance of the subsets ${}A$ and ${}B$.