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  "body": "\n## Summary\n\nA co-Heyting algebra is a bounded lattice with a difference operation $a \\setminus b$, the least element $c$ such that $a \\le b \\vee c$.\nIt is the order dual of a [[Heyting algebra|NG943XNQWH]]: turning a co-Heyting algebra upside down gives a Heyting algebra, and conversely.\nEvery co-Heyting algebra is a [[distributive lattice|0HM0HQCK6N]].\nThe closed sets of a topological space form a co-Heyting algebra, and co-Heyting algebras serve as algebraic models of paraconsistent logics.\n\n## Explanations\n\n### L1 human\n\nIn a Heyting algebra one asks for the largest element that, together with $a$, stays below $b$.\nIn a co-Heyting algebra one asks instead for the smallest piece $c$ that one must add to $b$ in order to cover $a$.\nThe picture is the family of closed sets of the plane, where $A \\setminus B$ is the closure of the ordinary set difference.\nFor example, on the real line, if $A = [0, 2]$ and $B = [1, 2]$, then the difference is $[0, 1]$, not $[0, 1)$, since it must be closed.\n",
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