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  "body": "\n## Summary\n\nA basic open set of the [[spectrum|FB45BHHA2J]] of a [[commutative ring|0310REJJY8]] $R$ is a set $D(f)$ of [[prime ideals|00MHHZ9SNE]] not containing a fixed element $f$.\nThese sets form a [[basis|0NA0732YAG]] of the [[Zariski topology|8SQK7RTB63]].\nThe set $D(f)$ is in natural bijection with the spectrum of the [[localization|4C1AE84N5N]] $R_f$, so basic open sets are again spectra of rings.\n\n## Explanations\n\n### L1 human\n\nThink of $f$ as a function on the space of prime ideals.\nThe basic open set $D(f)$ is the set of points where $f$ does not vanish.\nOn $\\operatorname{Spec} \\Z$, the set $D(6)$ consists of all points except $(2)$ and $(3)$.\nEvery open set is a union of such sets, just as every open set of the plane is a union of discs.\nThe [[definition|PS8DVS9WTA]] states this.\n",
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