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 $X\setminus E$.
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It can be shown that every net has a universal^{} subnet.

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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).
Title  ultranet 

Canonical name  Ultranet 
Date of creation  20130322 12:54:35 
Last modified on  20130322 12:54:35 
Owner  asteroid (17536) 
Last modified by  asteroid (17536) 
Numerical id  9 
Author  asteroid (17536) 
Entry type  Definition 
Classification  msc 54A20 
Synonym  universal net 
Related topic  Ultrafilter^{} 
Related topic  EveryNetHasAUniversalSubnet 