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 elementsa,bin the set, there is a third element which is larger than bothaandb. Also known as directed system; Moore-Smith set.

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(theory)

directed set - 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.