Scott continuity
id:
scott-continuity-321-12605822
title:
Scott continuity
text:
In mathematics, given two partially ordered sets P and Q, a function f: P → Q between them is Scott-continuous if it preserves all directed suprema. That is, for every directed subset D of P with supremum in P, its image has a supremum in Q, and that supremum is the image of the supremum of D, i.e. ⊔ f [ D ] = f , where ⊔ is the directed join. When Q is the poset of truth values, i.e. Sierpiński space, then Scott-continuous functions are characteristic functions of open sets, and thus Sierpiński
brand slug:
wiki
category slug:
encyclopedia
description:
Definition of continuity for functions between posets
original url:
https://en.wikipedia.org/wiki/Scott_continuity
date created:
date modified:
2024-01-06T09:40:50Z
main entity:
{"identifier":"Q895815","url":"https://www.wikidata.org/entity/Q895815"}
image:
fields total:
13
integrity:
14