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  "body": "\n## Statement\n\nLet $X$ be a [[topological space|0CNQXVBHCX]] and let $S \\subseteq X$.\nThen $S \\subseteq \\overline{S}$, the set $\\overline{S}$ is closed, and each closed set $F$ of $X$ with $S \\subseteq F$ satisfies $\\overline{S} \\subseteq F$.\n\n## Remarks\n\nHere $\\overline{S}$ is the [[closure|0DRKT1QJR7]] of $S$. That it is closed is the statement [[closure is closed|02TZDKG50Q]].\nThis is the dual of the statement that the [[interior is the largest open subset|0HAZEFH137]].\nIf $S \\subseteq T$, then $\\overline{S} \\subseteq \\overline{T}$.\n\n## Explanations\n\n### L1 human\n\nAmong all closed sets that contain $S$, the closure is the smallest one.\nFor example, each closed set that contains $(0, 1)$ in $\\mathbb{R}$ also contains $[0, 1]$.\n",
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