Definition:Strict Upper Closure/Set

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

Let $T \subseteq S$.

The strict upper closure of $T$ (in $S$) is defined as:


 * $T^\succ := \bigcup \left\{{t^\succ: t \in T}\right\}$

where $t^\succ$ denotes the strict upper closure of $t$ in $S$.

That is:
 * $T^\succ := \left\{ {u \in S: \exists t \in T: t \prec u}\right\}$

Also see

 * Definition:Strict Upper Closure of Element


 * Definition:Strict Lower Closure of Subset
 * Definition:Upper Closure of Subset