My answer is no because, $\mathbb{Q}^o = \emptyset$ and so $\overline{(\mathbb{Q}^o)} = \emptyset$ but $\overline{\mathbb{Q}} = \mathbb{R}$ and so $\big(\overline{\mathbb{Q}}\,\big)^o = \mathbb{R}$.
Is my example correct?
My answer is no because, $\mathbb{Q}^o = \emptyset$ and so $\overline{(\mathbb{Q}^o)} = \emptyset$ but $\overline{\mathbb{Q}} = \mathbb{R}$ and so $\big(\overline{\mathbb{Q}}\,\big)^o = \mathbb{R}$.
Is my example correct?