Definition:Upper Set/Definition 1

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $U \subseteq S$.

$U$ is an upper set in $S$ :


 * $\forall u \in U: \forall s \in S: u \preceq s \implies s \in U$

Also see

 * Equivalence of Definitions of Upper Set