Definition:Upper Set

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

Let $U \subseteq S$.

Also known as
An upper set is also known as an upper-closed set or upward-closed set. Some sources call it an upset or up-set.

Also see

 * Equivalence of Definitions of Upper Set


 * Definition:Lower Set
 * Definition:Upper Closure