Definition:Upper Section/Definition 2

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

Let $U \subseteq S$.

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


 * $U^\succeq \subseteq U$

where $U^\succeq$ is the upper closure of $U$.

Also see

 * Equivalence of Definitions of Upper Set