Definition:Universal Net

Definition
Let $S$ be a non-empty set.

Let $H$ be a set directed by $\preceq$.

Let $f \colon H \to S$ be a net in $S$.

Then $f$ is a universal net if and only if for each subset, $A$, of $S$, $f$ is eventually in $A$ or $f$ is eventually in $S \setminus A$