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)