transitive closure
1Transitive closure — In mathematics, the transitive closure of a binary relation R on a set X is the smallest transitive relation on X that contains R .For example, if X is a set of airports and xRy means there is a direct flight from airport x to airport y , then… …
2Closure — may refer to: Closure (container) used to seal a bottle, jug, jar, can, or other container Closure (wine bottle), a stopper Closure (business), the process by which an organization ceases operations Closure (philosophy), a principle in… …
3Transitive reduction — In mathematics, the transitive reduction of a binary relation R on a set X is a minimal relation R on X such that the transitive closure of R is the same as the transitive closure of R . If the transitive closure of R is antisymmetric and finite …
4Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …
5Transitive relation — In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b , and b is in turn related to an element c , then a is also related to c . Transitivity is a key property of both partial order… …
6Transitive set — In set theory, a set (or class) A is transitive, if * whenever x ∈ A , and y ∈ x , then y ∈ A , or, equivalently, * whenever x ∈ A , and x is not an urelement, then x is a subset of A .The transitive closure of a set A is the smallest (with… …
7Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y)   (cl… …
8Fermeture transitive —  Ne pas confondre avec la clôture transitive. La fermeture transitive est une opération mathématique pouvant être appliquée sur des ensembles. Sommaire 1 Théorie des ensembles 2 Théorie des graphes …
9Action algebra — In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to the former, while adding the left and right… …
10Binary relation — Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… …
