Definition:Property (S)

Definition
Let $L = \left({S, \preceq}\right)$ be an up-complete ordered set.

Let $X$ be a subset of $S$.

Then $X$ has property (S)
 * for all directed subsets $D$ of $S$: $\sup D \in X \implies \exists y \in D:\forall x \in D: y \preceq x \implies x \in X$