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). (1995-02-03)

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