If $0<\|x-y\|$ , can I say that there exists $0
As a consequence of Archimedean property of $\mathbb{R} $, $ \exists M \in \mathbb{R} $ such that $ 0 < M < \|x−y\|$. Can I say that when any fixed $x\in \overline{A}=A\subset \mathbb{R}^{n}$ and any $y\in A^{c}$, if $ M:=\min\|x-y\|$, then $0 < M \le \|x−y\|$?
$\|\cdot\|$ : Euclidean norm on $\mathbb{R}^{n}$.