The question is,
Let $(P,\le)$ be a poset and $S,T\subseteq P$ such that the following holds, $$\forall t\forall s(t\in T\land s\in S\to s\le t)$$does this type of relation between $S$ and $T$ has a standard name?
I thought about phrasing the property as saying that "each element of $T$ dominates $S$". But it would surely be good if there is a standrad terminology (and if possible some standard notation as well) for it.
$S$ is the set of lower bounds of $T$,
$T$ is the set of upper bounds of $S$.
It is a generalization of a Dedekind cut.