Let $X$ denote a topological space. Can we characterize the filters on $X$ that arise as the eventuality filter of a sequence?
2026-02-22 21:59:15.1771797555
Which sequences arise as the eventuality filter of a sequence?
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It's clear that such an eventuality filter of a sequence must contain a countable set $A \in \mathcal{F}$.
Look at the set of all countable subsets of $A$. These have empty intersection or some countable or finite intersection. Try to think of a sequence that has tails that behave like that.