A set S, a subset of D, is Scott-closed if
(1) If Y is a subset of S and Y is directed then lub Y is in S and
(2) If y <= s in S then y is in S.
I.e. a Scott-closed set contains the lubs of its directed subsets and anything less than any element. (2) says that S is downward closed (or left closed).
("<=" is written in LaTeX as \sqsubseteq).
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Nearby terms: SCOPE « scope « Scorpion « Scott-closed » Scott domain » SCPI » SCPI Consortium