Definition:Lower Section/Definition 2

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

Let $L \subseteq S$.

$L$ is a lower section in $S$ :
 * $L^\preceq \subseteq L$

where $L^\preceq$ is the lower closure of $L$.

Also see

 * Equivalence of Definitions of Lower Section