Let $F$ be a non-empty closed set of $E$ and $u$ in $E$. Show that there exists $v$ in $F$ such that $$\forall w \in F, \quad \|u - v\| \leqslant \|u - w\|$$
Let $F$ be a non-empty closed set of $E$ and $u$ in $E$. Show that there exists $v$ in $F$ such that
$$\forall w \in F, \quad \|u - v\| \leqslant \|u - w\|$$