Definition:Directed Preordering

Definition
Let $\left({S, \precsim}\right)$ be a preordered set.

Then $\left({S, \precsim}\right)$ is a directed set iff:


 * $\forall x, y \in S: \exists z \in S: x \precsim z$ and $y \precsim z$

Also see

 * Definition:Directed Subset