A partial order is related upper half bandage ( English conditional upper semi-lattice , in short CUSL ) if each couple has a supremum limited, so if all the following applies: If there with , then there exists a least upper bound .
Be a Cusl. A non-empty subset is called an ideal of if:
is closed at the bottom, d. H. for , and holds .
Are in limited, d. H. there is one with so is .
properties
Obviously every association is a cusl; in an association is defined as .
The general definition includes that of associations.
^ Viggo Stoltenberg-Hansen, Ingrid Lindstrom and Edward R. Griffor: Mathematical theory of domains. Cambridge Tracts in Theoretical Computer Science, 1994.