Definition:Upper Section/Definition 1

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Let $U \subseteq S$.

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


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

Also see

 * Equivalence of Definitions of Upper Section