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  "body": "\n## Summary\n\nAn interior operator on a [[partially ordered set|011C29Q1S1]] is a map that is deflationary, monotone and idempotent.\nIt is the dual of a [[closure operator|17FVAN6HXX]]: it sends each element to the greatest \"open\" element below it.\nThe [[interior|0C38S0KMJK]] of a subset of a topological space is the main example.\nInterior operators are also called kernel operators.\n\n## Explanations\n\n### L1 human\n\nAn interior operator shrinks an element to the largest element of a special kind inside it.\nIn the plane, the interior of a closed disc is the open disc: remove the boundary circle.\nTaking the interior again changes nothing, and a smaller set has a smaller interior.\nThese three features define an interior operator.\n",
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