directed set


directed set

[də′rek·təd ′set] (mathematics) A partially ordered set with the property that for every pair of elements a,b in the set, there is a third element which is larger than both a and b. Also known as directed system; Moore-Smith set.

directed set

(theory)A set X is directed under some relation, <= (lessthan or equal), if it is non-empty and if for any two elementsx and y there exists an element z such that x <= z and y <= z.I.e. all pairs have an upper bound.