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  "body": "\n## Summary\n\nThe Zariski topology is a topology on the [[spectrum|FB45BHHA2J]] of a [[commutative ring|0310REJJY8]].\nIts closed sets are the sets of [[prime ideals|00MHHZ9SNE]] containing a given set of elements.\nOn an affine variety it restricts to the topology whose closed sets are the zero sets of polynomials.\nIt has few open sets: it is [[quasi-compact|J4YW23MD6N]] and usually not [[Hausdorff|0S1FJ8VEX9]].\nIt is the topology used throughout algebraic geometry.\n\n## Explanations\n\n### L1 human\n\nIn the Zariski topology a closed set is a set of common zeros of some functions.\nOn the line $\\C$, the zero set of a nonzero polynomial is finite, so the closed subsets of the line are the finite sets and the whole line.\nAny two nonempty open sets then meet, which is very different from the usual topology.\nOn $\\operatorname{Spec} R$ one says that $f$ \"vanishes\" at a prime $\\mathfrak p$ when $f \\in \\mathfrak p$.\nThe [[definition|EXJAXVXW51]] uses this to define the closed sets.\n",
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