closure operator in a sentence

Examples

1. Therefore, the abstract theory of closure operators and the Kuratowski closure axioms can be easily translated into the language of interior operators, by replacing sets with their complements.
2. "Comments " : The Kuratowski closure axioms abstract the properties of the closure operator on a topological space, which assigns to each subset its topological closure.
3. A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator.
4. The orthogonal complement generalizes to the annihilator, and gives a Galois connection on subsets of the inner product space, with associated closure operator the topological closure of the span.
5. *PM : upper set operation is a closure operator, id = 8908 new !-- WP guess : upper set operation is a closure operator-- Status:
6. *PM : upper set operation is a closure operator, id = 8908 new !-- WP guess : upper set operation is a closure operator-- Status:
7. This topological closure operator has been generalized in category theory; see " Categorical Closure Operators " by G . Castellini in " Categorical Perspectives ", referenced below.
8. This topological closure operator has been generalized in category theory; see " Categorical Closure Operators " by G . Castellini in " Categorical Perspectives ", referenced below.
9. Another representation is obtained by noting that the image of any closure operator on a complete lattice is again a complete lattice ( called its " closure system " ).
10. Given a Galois connection with lower adjoint and upper adjoint, we can consider the compositions, known as the associated closure operator, and, known as the associated kernel operator.