In mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other words, it is a non-empty preordered set A {\displaystyle A} such that for any a {\displaystyle a} and b {\displaystyle b} in A {\displaystyle A} there exists c {\displaystyle c} in A {\displaystyle A} with a ≤ c {\displaystyle a\leq c} and b ≤ c {\displaystyle b\leq c} .
In mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other words, it is a non-empty preordered set A {\displaystyle A} such that for any a {\displaystyle a} and b {\displaystyle b} in A {\displaystyle A} there exists c {\displaystyle c} in A {\displaystyle A} with a ≤ c {\displaystyle a\leq c} and b ≤ c {\displaystyle b\leq c} .
Source: Wikipedia "Directed set" · CC BY-SA 4.0
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