Distance to a set
= Distance to a set
For a metric space, $d(x,S)=\inf_{s\in S}d(x,s)$ is $1$-Lipschitz and vanishes on the closure of $S$.
= Distance to a set
For a metric space, $d(x,S)=\inf_{s\in S}d(x,s)$ is $1$-Lipschitz and vanishes on the closure of $S$.