A filter that is maximal as a set with respect to the definition of .
In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged. An ultrafilter may be considered as a finitely additive measure. Then every subset of X is either considered "almost everything" or "almost nothing". If A is a subset of X, then either A or X \ A is an element of the ultrafilter. The concept can be generalized to Boolean algebras or even to general partial orders, and has many applications in set theory, model theory, and topology.
The numerical value of ultrafilter in Chaldean Numerology is: 3
The numerical value of ultrafilter in Pythagorean Numerology is: 7
Images & Illustrations of ultrafilter
Find a translation for the ultrafilter definition in other languages:
Select another language:
Discuss these ultrafilter definitions with the community:
Word of the Day
Would you like us to send you a FREE new word definition delivered to your inbox daily?
Use the citation below to add this definition to your bibliography:
"ultrafilter." Definitions.net. STANDS4 LLC, 2018. Web. 24 Feb. 2018. <https://www.definitions.net/definition/ultrafilter>.