Closure_of_Open_Ball_in_Metric_Space

Let $M = \struct {A, d}$ be a metric space. Let $\map {B_\epsilon} x$ be an open $\epsilon$-ball in $M$. Let $y \in \map \cl {\map {B_\epsilon} x}$, where $\cl$ denotes the closure of $\map {B_\epsilon} x$. Then $\map d {x, y} \le \epsilon$.