directed set(redirected from Upward-directed set)
directed set[də′rek·təd ′set]
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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.
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