Definition:Element is Way Below

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

Let $x, y \in S$.

Then $x$ is way below $y$, denoted $x \ll y$, :
 * for every directed subset $D$ of $S$:
 * if $D$ admits a supremum and $y \preceq \sup D$
 * then there exists $d \in D$ such that $x \preceq d$