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  "body": "\n## Summary\n\nA quasi-compact morphism of schemes is one for which the preimage of every open affine subscheme is quasi-compact.\nQuasi-compact means that every open cover has a finite subcover; no Hausdorff condition is asked.\nIt is a finiteness condition on a [[morphism of schemes|JXRKH6P1Z4]].\nIt is part of the definition of morphisms of finite type and of proper morphisms.\n\n## Explanations\n\n### L1 human\n\nSpaces in algebraic geometry are rarely Hausdorff, so \"compact\" is replaced by \"quasi-compact\": every open cover has a finite subcover.\nEvery affine scheme is quasi-compact.\nA morphism is quasi-compact when, over each affine piece of the target, the source can be covered by finitely many affine pieces.\nMapping infinitely many separate points onto a single point fails this test.\n",
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