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  "body": "\n## Statement\n\nLet $X$ be a [[topological space|0CNQXVBHCX]] and let $S \\subseteq X$.\nThen $\\operatorname{int} S \\subseteq S$, the set $\\operatorname{int} S$ is open, and each open set $U$ of $X$ with $U \\subseteq S$ satisfies $U \\subseteq \\operatorname{int} S$.\n\n## Remarks\n\nHere $\\operatorname{int} S$ is the [[interior|0C38S0KMJK]] of $S$. The openness is the statement [[interior is open|0PNWCM559P]].\nA consequence: $S$ is open if and only if $\\operatorname{int} S = S$.\nIf $S \\subseteq T$, then $\\operatorname{int} S \\subseteq \\operatorname{int} T$.\n\n## Explanations\n\n### L1 human\n\nAmong all open sets inside $S$, the interior is the biggest one.\nEach open set inside $S$ is already inside the interior.\n",
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