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Filters (and ultrafilters) are used in various areas of mathematics, e.g. general topology, set theory, boolean algebras, model theory. In topology they can be used to study convergence in a more general way than just convergence of sequences.

Filters (and ultrafilters) are used in various areas of mathematics, e.g. general topology, set theory, boolean algebras, model theory. The idea behind filters is to model the notion of a "large set" with respect to some property.

In topology they can be used to study convergence in a more general way than just convergence of sequences.

Various types of ultrafilters (such as good ultrafilters, Ramsey ultrafilters, P-points) are useful in set theory and model theory and their applications.

The notion of a filter can be generalized to partial orders, which is a useful notion in forcing, for example.

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