Computing (FOLDOC) dictionary

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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

directedsubsets and anything less than any element. (2) says that S

is downward

closed (or left closed).