What is the closure, interior and boundary of $\mathbb{Q}$ in ($\mathbb{R}$,d) a discrete metric space and how to interpret or prove this?
2026-04-06 14:52:36.1775487156
$\mathbb{Q}$ closure, interior and boundary in ($\mathbb{R}$,d)
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If $(\mathbb{R},d)$ is a discrete metric space, then every subset of $\mathbb{R}$ is both open and closed with respect to the given metric.
Thus every subset $X \subseteq \mathbb{R}$ satisfies the following. Interior of $X$ is equal to $X$. Closure of $X$ is equal to $X$ and the boundary of $X$ is equal to the empty set.