A set S, a subset of D, is Scott-closed if (1) If Y is a subset of S and Y is href="module.php?name=Lexikon&file=search&eid=1&query=directed">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 href="module.php?name=Lexikon&file=search&eid=1&query=lub">lubs of its href="module.php?name=Lexikon&file=search&eid=1&query=directed">directed subsets and anything less than any element. (2) says that S is downward href="module.php?name=Lexikon&file=search&eid=1&query=closed">closed (or left closed). ("<=" is written in href="module.php?name=Lexikon&file=search&eid=1&query=LaTeX">LaTeX as href="module.php?name=Lexikon&file=search&eid=1&query=sqsubseteq">sqsubseteq). (1995-02-03)

In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=411">ai ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1606">bs ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2138">cl ] [ href="module.php?name=Lexikon&op=content&tid=2196">closed set ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2545">con ] [ href="module.php?name=Lexikon&op=content&tid=2976">D ] [ href="module.php?name=Lexikon&op=content&tid=3565">do ] [ href="module.php?name=Lexikon&op=content&tid=3649">down ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=4008">element ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5656">hing ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6449">ir ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6989">LaTeX ] [ href="module.php?name=Lexikon&op=content&tid=7081">less than ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7351">lose ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7417">lub ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=10999">say ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11281">set ] [ href="module.php?name=Lexikon&op=content&tid=11900">sqsubseteq ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12148">subseteq ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12896">tt ] [ href="module.php?name=Lexikon&op=content&tid=13891">X ] [ href="module.php?name=Lexikon&op=content&tid=14024">Y ] [ href="module.php?name=Lexikon&op=content&tid=14075">yt ]