Definition:Lower Set

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

Let $L \subseteq S$.

Also known as
A lower set is also known as a lower-closed set or downward-closed set. Some sources call it a downset or down-set.

Also see

 * Equivalence of Definitions of Lower Set


 * Definition:Lower Closure
 * Definition:Upper Set