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  "body": "\n## Summary\n\nA Scott domain is a directed-complete partial order that is algebraic and bounded complete.\nAlgebraic means that every element is the directed supremum of the [[compact elements|9F7TYES4KE]] below it.\nBounded complete means that every subset with an upper bound has a supremum.\nThey come from the work of Dana Scott on the semantics of programming languages and of the [[lambda calculus|BD756KR8FM]].\nThey form a cartesian closed category with Scott-continuous maps.\n\n## Explanations\n\n### L1 human\n\nA Scott domain is a space of pieces of information in which every piece is a limit of finite pieces.\nTwo pieces that are consistent, meaning that some piece extends both, can always be combined into a least common extension.\nThe partial functions from $\\N$ to $\\N$ form a Scott domain, with the finite partial functions as compact elements.\nTwo partial functions that agree on their common domain combine by union.\nBecause maps between Scott domains again form a Scott domain, one can build domains of functions, of functions of functions, and so on.\n",
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