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Meaning of SCOTT-CLOSED

 
Computing Dictionary
 
 Definition: 

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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