Set of lower bounds in poset is defined like $ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.
Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?
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Sign up to join this communitySet of lower bounds in poset is defined like $ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap_{a \in A} \{ x \in P : x \le a \}$.
Is there in literature a name for union $ \bigcup_{a \in A} \{ x \in P : x \le a \} $?
Introduction to Lattices and Order by B. A. Davey and H. A. Priestly calls this $\mathord{\downarrow}A$ or the downset of $A$ and also uses $\mathord{\downarrow} a$ for $\{x \in P : x \le a\}$