Definition:Bounded Above Set

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

A subset $T \subseteq S$ is bounded above (in $S$) iff $T$ admits an upper bound (in $S$).

Otherwise, $T$ is unbounded above (in $S$).

Also see

 * Definition:Upper Bound (Ordered Set)
 * Definition:Bounded Below Set
 * Definition:Lower Bound (Ordered Set)
 * Definition:Bounded Set