Scott-closed

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)