Metric space/Distance/Subsets/Infimum/Definition

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

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

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