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  "body": "\n## Summary\n\nA sober space is a topological space in which every irreducible closed set is the closure of exactly one point.\nThat point is called the generic point of the set.\nEvery sober space is $T_0$, and every Hausdorff space is sober.\nSpectra of commutative rings with the Zariski topology are sober.\nA sober space can be recovered, up to homeomorphism, from its lattice of open sets.\n\n## Explanations\n\n### L1 human\n\nSome closed sets cannot be split into two smaller closed pieces; they are called irreducible.\nA sober space has, for each such set, one special point whose closure is the whole set.\nIn algebraic geometry, the irreducible curve $y = x^2$ in the plane has such a point in the spectrum of the polynomial ring: the prime ideal $(y - x^2)$.\nIn a Hausdorff space, the only irreducible closed sets are single points, so each is its own generic point.\n",
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