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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]].\nA subset $F$ of $X$ is closed in $X$ when its [[complement|0B1FSS1VZW]] $X \\setminus F$ is [[open|01ZQQDCERP]] in $X$.\n\n## Remarks\n\nThe sets $\\emptyset$ and $X$ are both open and closed.\nA set can be neither open nor closed: $[0, 1)$ in $\\mathbb{R}$ is an example.\nIn a metric space, $F$ is closed if and only if it [[contains the limits of its convergent sequences|09GQ3ZTQJ9]].\n\n## Explanations\n\n### L1 human\n\nClosed is not the opposite of open. A closed set is a set whose outside is open.\nThe interval $[0, 1]$ is closed in $\\mathbb{R}$, because its outside $(-\\infty, 0) \\cup (1, \\infty)$ is open.\n",
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