Definition:Directed Preordering

Definition
Let $D$ be a set, and let $\leq$ be a preordering on $D$.

Suppose that furthermore:


 * $\forall a,b \in D: \exists c \in D: \left({a \leq c}\right) \land \left({b \leq c}\right)$

Then $\left({D, \leq}\right)$ is said to be a directed set.