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  "body": "\n## Summary\n\nThe Scott topology on a partially ordered set has as open sets the up-closed sets that cannot be reached by a directed supremum from outside.\nIt turns a [[directed-complete partial order|7TSXP95QN6]] into a topological space whose continuous maps are the Scott-continuous maps.\nIts [[specialization preorder|CMYVK9CEKZ]] is the original order, so the order can be recovered from the topology.\nIt is the topology used in [[domain theory|Q2P5D74Q1V]].\n\n## Explanations\n\n### L1 human\n\nAn open set in the Scott topology is an \"observable property\" of partial information.\nIf an element has the property, then every better-informed element has it too, so open sets are closed upward.\nAnd if a limit of approximations has the property, then some approximation already has it, since one can only observe finitely much.\nFor example, in $\\N \\cup \\set{\\infty}$, the set $\\set{\\infty}$ is not Scott-open, because $\\infty$ is the supremum of $0, 1, 2, \\ldots$, none of which is in the set; but every set $\\set{n, n + 1, \\ldots, \\infty}$ is Scott-open.\n",
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