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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]], let $S \\subseteq X$ and let $x \\in S$.\nThe point $x$ is an isolated point of $S$ when there is an [[open set|01ZQQDCERP]] $U$ of $X$ with $U \\cap S = \\{x\\}$.\n\n## Remarks\n\nEach point of $S$ is either an isolated point of $S$ or a [[limit point|0HBQC2GJXT]] of $S$, and not both.\nIn $\\mathbb{R}$, each point of $\\mathbb{Z}$ is an isolated point of $\\mathbb{Z}$: take $U = (n - 1/2, n + 1/2)$.\nA point $x$ is an isolated point of $X$ itself if and only if $\\{x\\}$ is open.\n\n## Explanations\n\n### L1 human\n\nAn isolated point is a point of the set that stands alone: a small region about it contains no other point of the set.\nIn the set $\\{0\\} \\cup [1, 2]$, the point $0$ is isolated, but $1$ is not.\n",
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