ultrafilter

== English == === Etymology === From ultra- +‎ filter. === Noun === ultrafilter (plural ultrafilters) A device that performs ultrafiltration. (mathematics, of a set, whose subsets are partially ordered by inclusion) A proper filter which has a law of dichotomy for complements. (mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter. ==== Hypernyms ==== filter ==== Hyponyms ==== free ultrafilter principal ultrafilter ==== Holonyms ==== poset ==== Translations ==== === Verb === ultrafilter (third-person singular simple present ultrafilters, present participle ultrafiltering, simple past and past participle ultrafiltered) (transitive) To filter by ultrafiltration. ==== Derived terms ==== ==== Further reading ==== ultrafilter on Wikipedia.Wikipedia