The closed sets can be determined from the closure operator; a set is closed if it is equal to its own closure.
22.
A "'Galois insertion "'of into is a Galois connection in which the closure operator is the identity on.
23.
The compositions and are the associated closure operators; they are monotone idempotent maps with the property for all in and for all in.
24.
The set " S " must be a subset of a closed set in order for the closure operator to be defined.
25.
*PM : properties of the closure operator, id = 4474-- WP guess : properties of the closure operator-- Status:
26.
*PM : properties of the closure operator, id = 4474-- WP guess : properties of the closure operator-- Status:
27.
*PM : properties of the closure operator, id = 7075-- WP guess : properties of the closure operator-- Status:
28.
*PM : properties of the closure operator, id = 7075-- WP guess : properties of the closure operator-- Status:
29.
Since the identity function is a closure operator too, this shows that the complete lattices are exactly the images of closure operators on complete lattices.
30.
Since the identity function is a closure operator too, this shows that the complete lattices are exactly the images of closure operators on complete lattices.
