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  "body": "\n## Summary\n\nA hyperconnected space, also called an irreducible space, is a nonempty [[topological space|0CQHFPGJ45]] in which any two nonempty open sets meet.\nEquivalently, it is not the union of two proper closed subsets.\nEvery hyperconnected space is [[connected|0V032VWTHD]], but the condition is much stronger.\nIrreducible spaces are basic in algebraic geometry, where irreducible varieties and the spectra of integral domains have this property.\n\n## Explanations\n\n### L1 human\n\nIn a hyperconnected space, every nonempty open set is spread all over the space: it is dense.\nThis never happens in a Hausdorff space with two or more points, where two points have disjoint neighbourhoods.\nAn infinite set with the [[cofinite topology|0B906ZBTMZ]] is hyperconnected, since two nonempty open sets miss only finitely many points each.\nSuch coarse topologies appear naturally as Zariski topologies in algebraic geometry.\n",
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