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).