Definition:Strict Lower Closure/Element

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

Let $a \in S$.

The strict lower closure of $a$ (in $S$) is defined as:
 * $a^\prec := \set {b \in S: b \preccurlyeq a \land a \ne b}$

or:
 * $a^\prec := \set {b \in S: b \prec a}$

That is, $a^\prec$ is the set of all elements of $S$ that strictly precede $a$.

Also see

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