Suppose that $A$ is a poset, and $B\subseteq A$ such that:
$$\forall b \in B,\forall a\in A: a<b\Rightarrow a\in B$$
This set has a special name. I studied properties of this set in my class, but we called it in a really weird name. I can’t find the name of the set in English. Can someone tell me what is the name of the set in English?
Thanks.