directed set

(redirected from Upward 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, <= (less than or equal), if it is non-empty and if for any two elements x and y there exists an element z such that x <= z and y <= z. I.e. all pairs have an upper bound.