A net $(x_a)_{a\in A}$ on a set $X$ is said to be an ultranet or universal net if whenever $E\subseteq X$ $(x_a)$ is either eventually in $E$ or eventually in $X\smallsetminus E$

Properties:

• It can be shown that every net has a universal subnet.
• When $X$ is a locally compact topological space, a universal net in $X$ is either convergent or it ``goes to infinity'' (it eventually leaves every compact subset).