# closure operator in a sentence

### Examples

- Such a least cut does indeed exist and one has a
*closure operator*on the powerset lattice of all elements. - Any Galois connection gives rise to
*closure operators*and to inverse order-preserving bijections between the corresponding closed elements. - If the
*closure operator*is taken as primitive, the interior operator can be defined as " x" - A set together with a
*closure operator*on it is sometimes called a "'closure system " '. - The convex hull in " n "-dimensional Euclidean space is another example of a finitary
*closure operator*. - Boolean interior algebras can be identified with ordinary Boolean algebras as their interior and
*closure operators*provide no meaningful additional structure. - Every Galois connection ( or residuated mapping ) gives rise to a
*closure operator*( as is explained in that article ). - The operator \ langle \ rangle is a finitary
*closure operator*on the set of subsets of | \ mathcal A |. - In summary, one can say that every complete lattice is isomorphic to the image of a
*closure operator*on a powerset lattice. - In this way,
*closure operators*and Galois connections are seen to be closely related, each specifying an instance of the other.