A closed set $O$ is a subset of the real numbers such that $\exists x \in O, \forall \epsilon>0$ s.t. $(x-\epsilon,x+\epsilon)$ is not a subset of $O$.
Are the only two $x \in O$ s.t. $(x-\epsilon,x+\epsilon)$ is not a subset of $O$, the infimum/minimum or the supremum/maximum of that set $O$?