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  "body": "\n## Summary\n\nThe closure of a closable operator is its smallest closed extension.\nIts graph is the closure of the graph of the original operator.\nTaking closures lets one define an operator on a simple domain and then pass to a closed operator, to which the main theorems apply.\n\n## Explanations\n\n### L1 human\n\nAn operator given by a formula on nice inputs can be extended by limits: if $x_n \\to x$ and $T x_n \\to y$, declare $Tx = y$.\nFor a closable operator this rule is consistent, and the result is the closure.\nFor example, starting with differentiation on polynomials in $C[0, 1]$, the closure is differentiation on all continuously differentiable functions.\nIt is the most economical way to make an operator closed without changing what it does on the old domain.\n",
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