Source: wikibot/ultrafilter-on-a-set
= Ultrafilter on a set
{wiki=Ultrafilter_on_a_set}
An **ultrafilter** on a set \\( X \\) is a special type of filter that has additional properties, particularly in topology and set theory. Here's a precise definition and some key properties: 1. **Filter**: A filter \\( \\mathcal\{F\} \\) on a set \\( X \\) is a collection of subsets of \\( X \\) such that: - The empty set is not in \\( \\mathcal\{F\} \\).