# Category:Filter Theory

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This category contains results about **Filter Theory**.

Definitions specific to this category can be found in Definitions/Filter Theory.

**Filter Theory** is a branch of topology which studies filters.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Filter Theory"

The following 23 pages are in this category, out of 23 total.

### E

- Equivalence of Definitions of Continuous Mapping between Topological Spaces/Point
- Equivalence of Definitions of Filter on Set
- Equivalence of Definitions of Ultrafilter on Set
- Equivalence of Definitions of Ultrafilter on Set/Definition 1 iff Definition 3
- Equivalence of Definitions of Ultrafilter on Set/Equivalence of Definitions 1, 2 and 3
- Every Ultrafilter Converges implies Every Filter has Limit Point
- Existence of Nonprincipal Ultrafilter

### F

- Filter Basis Generates Filter
- Filter is Finer iff Sets of Basis are Subsets
- Filter on Product of Hausdorff Spaces Converges iff Projections Converge
- Filter on Product Space Converges iff Projections Converge
- Filter on Product Space Converges to Point iff Projections Converge to Projections of Point
- Filter on Set is Proper Filter