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  "body": "\n## Summary\n\nA limit point compact space is a topological space in which every infinite subset has a [[limit point|0E3X7TXS67]].\nIt is the form of compactness that appears in the Bolzano–Weierstrass theorem.\nEvery [[countably compact|S3N3CHZV89]] space is limit point compact, and the two notions agree for T1 spaces.\nFor metric spaces, it is equivalent to compactness.\n\n## Explanations\n\n### L1 human\n\nIf you put infinitely many points in a limit point compact space, they must pile up somewhere.\nThere is a point whose every neighbourhood contains points of the set other than itself.\nFor example, in $[0, 1]$ any infinite set of points accumulates somewhere, by the Bolzano–Weierstrass theorem.\nIn $\\R$ this fails: the integers are infinite but do not accumulate anywhere.\n",
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