Definition:Inaccessible by Directed Suprema

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

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

Then $X$ is inaccessible by directed suprema
 * for all directed subsets $D$ of $S$: $\sup D \in X \implies X \cap D \ne \varnothing$