Definition:Lower Closure/Element/Class Theory

Definition
Let $A$ be a class under an ordering $\preccurlyeq$.

Let $a \in A$.

The lower closure of $a$ (in $A$) is defined as:


 * $a^\preccurlyeq := \set {b \in A: b \preccurlyeq a}$

Also see

 * Definition:Strict Lower Closure of Element (Class Theory)