Open sets

True or False: There exists a metric space which has an open singleton subset.

Definition: A set $U \subseteq X$ is open when every point $x \in X$ is an interior point of $X$ , i.e, for all $x \in U$ , there is an $\varepsilon > 0$ such that the entire collection of all elements $y \in X$ contained within an $\varepsilon$ radius of $x$ are still in $U$ .