Prove or disprove $bd(E)$ is nowhere dense for $E \subseteq X$ complete metric space

Question

I know this is not true but need to find an example of complete metric space $X$ with subset $E$ such that $\overline{bd(E)}$ has non-empty interior.

Answer 1

The boundary of $\mathbb{Q}$ in $\mathbb{R}$ (usual metric) is $\mathbb{R}$. The boundary of an open set (or equivalently a closed set) is nowhere dense.