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 I.e. a Scott-closed set contains the lub s of its directed subsets and anything less than any element. (2) says that S is downward closed (or left closed).
(" LaTeX as \sqsubseteq ).
(1995-02-03)