if :

$\displaystyle y\in\overline{S(x)}r$ then d(x,y) $\displaystyle \leq r $ and give an example to show that the converse is not always true .

{ $\displaystyle \overline{S(p)}r$ is not necessary equal to $\displaystyle \mbox{A}= $ $\displaystyle {\{ x \in X : d(x,y) \leq r }\} $ }