scott-closed

1 definition found

scott-closed - Free On-line Dictionary of Computing (26 May 2007) :

  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)