Directed set

In mathematics, a directed set is a nonempty set A together with a reflexive and transitive binary relation ≤ having the additional property that for any two elements a and b in A, there exists an element c in A (not necessarily distinct from a,b) with a ≤ c and b ≤ c (directedness).
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<theory> A set X is directed under some relation, upper bound.
(1994-11-11)