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).
Last updated: 1995-02-03