scott-closed

from The Free On-line Dictionary of Computing (8 July 2008)
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)
    

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