ultranet

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 $X\setminus E$.

:

• 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 ” (it eventually leaves every compact subset).