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  "body": "\n## Summary\n\nA Stone space is a [[compact|0TVJZYB6SH]] [[Hausdorff|0S1FJ8VEX9]] [[totally disconnected|0RJSBR9GW1]] topological space.\nStone spaces are also called Boolean spaces or profinite spaces.\nThey are exactly the spaces of ultrafilters of Boolean algebras, by [[Stone's representation theorem|S4QJ395PA5]], and [[Stone duality|B9T33D5MJK]] makes the two theories equivalent.\nThe Cantor set and the profinite groups are standard examples.\n\n## Explanations\n\n### L1 human\n\nA Stone space is compact, so it is \"small\" in the topological sense, but it is also completely broken into dust: no two points are connected.\nIts open sets are generated by sets that are open and closed at the same time.\nThe Cantor set is the typical picture: it is closed and bounded, yet any two of its points can be split by a gap.\nEvery finite set with the discrete topology is a Stone space too.\n",
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