Definition:Approximating Relation

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

Let $\RR$ be a relation on $S$.

Then $\RR$ is an approximating relation on $S$
 * $\forall x \in S: x = \map \sup {x^\RR}$

where $x^\RR$ denotes the $\RR$-segment of $x$.