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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]] and let $S \\subseteq X$.\nThe interior of $S$ is the [[union|05GK32H72H]] of all [[open sets|01ZQQDCERP]] $U$ of $X$ with $U \\subseteq S$.\nIt is written $\\operatorname{int} S$ or $S^\\circ$.\nA point of $\\operatorname{int} S$ is an interior point of $S$.\n\n## Remarks\n\nA point $x$ is an interior point of $S$ if and only if there is an open set $U$ with $x \\in U \\subseteq S$.\nIn a metric space, $x$ is an interior point of $S$ if and only if $B(x, \\varepsilon) \\subseteq S$ for some $\\varepsilon \u003e 0$.\nIn $\\mathbb{R}$, the interior of $[0, 1]$ is $(0, 1)$, and the interior of $\\mathbb{Q}$ is $\\emptyset$.\n\n## Explanations\n\n### L1 human\n\nThe interior of a set is what remains when you remove its edge points.\nA point is in the interior when a whole small neighbourhood of it lies in the set.\n",
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