Metric space/Open subset/Epsilon/Definition

Open set in a metric space

Let ${}(M,d)$ be a metric space. A subset ${}U\subseteq M$ is called open (in $(M,d)$), if for every ${}x\in U$ there exists an ${}\epsilon >0$ such that

${}U{\left(x,\epsilon \right)}\subseteq U\,$

holds.