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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]] and let $A \\subseteq X$.\nThe set $A$ is nowhere dense in $X$ when the [[interior|0C38S0KMJK]] of its [[closure|0DRKT1QJR7]] is empty, that is, $\\operatorname{int} \\overline{A} = \\emptyset$.\n\n## Remarks\n\nThe set $\\mathbb{Z}$ is nowhere dense in $\\mathbb{R}$. So is each finite subset of $\\mathbb{R}$.\nThe [[Cantor set|0BXNDZFQME]] is nowhere dense in $\\mathbb{R}$, though it is uncountable.\nThe set $\\mathbb{Q}$ is not nowhere dense in $\\mathbb{R}$, because its closure is $\\mathbb{R}$.\nA closed set is nowhere dense if and only if its complement is open and [[dense|0D198GPMTJ]].\n\n## Explanations\n\n### L1 human\n\nA nowhere dense set is thin everywhere: inside each open set, you can find a smaller open set that misses it completely.\nThe integers on the real line are an example, since there are gaps between them.\n",
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  "name": "Nowhere dense set",
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