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  "body": "\n## Summary\n\nThe derived set of a subset $A$ of a [[topological space|0CQHFPGJ45]] is the set of all [[limit points|0E3X7TXS67]] of $A$.\nIt is written $A'$.\nThe [[closure|0QEAJB91GZ]] of $A$ is $A \\cup A'$, and repeating the operation $A \\mapsto A'$ leads to the Cantor–Bendixson analysis of closed sets.\n\n## Explanations\n\n### L1 human\n\nA limit point of $A$ is a point that has points of $A$, other than itself, arbitrarily close to it.\nThe derived set collects all such points, whether they lie in $A$ or not.\nFor the set $A = \\set{1, 1/2, 1/3, \\dots}$ in $\\R$, every point of $A$ is alone in a small interval, but the points pile up at $0$.\nSo the derived set of $A$ is $\\set{0}$.\n",
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