Ultrafilter (set theory)
In the mathematical field of set theory, an ultrafilter is a maximal proper filter: it is a filter on a given non-empty set which is a certain type of non-empty family of subsets of that is not equal to the power set of (such filters are called proper) and that is also "maximal" in that there does not exist any other proper filter on that contains it as a proper subset. Said differently, a proper filter is called an ultrafilter if there exists exactly one proper filter that contains it as a subset, that proper filter (necessarily) being itself.
Algebraic closureAmorphous setAxiom of choiceBanach limitBanach–Alaoglu theoremBanach–Tarski paradoxBasis (linear algebra)Boolean prime ideal theoremCardinal characteristic of the continuumCauchy spaceCompact spaceCompactly generated spaceCompactness theoremConvergence spaceDimension theorem for vector spacesDiscrete spaceEduard HellyField (mathematics)Field of setsFilters in topologyFinite intersection propertyFréchet filterFølner sequenceHahn–Banach theoremHyperreal numberInvariant basis numberLindenbaum's lemmaList of lemmasList of mathematical proofsList of order theory topicsMartin measureNet (mathematics)Partition regularityPrincipal ultrafilterProduct topologyRamsey ultrafilterRudin-Keisler equivalentRudin-Keisler orderRudin-Keisler orderingRudin–Keisler equivalent
Link from a Wikipage to another Wikipage
primaryTopic
Ultrafilter (set theory)
In the mathematical field of set theory, an ultrafilter is a maximal proper filter: it is a filter on a given non-empty set which is a certain type of non-empty family of subsets of that is not equal to the power set of (such filters are called proper) and that is also "maximal" in that there does not exist any other proper filter on that contains it as a proper subset. Said differently, a proper filter is called an ultrafilter if there exists exactly one proper filter that contains it as a subset, that proper filter (necessarily) being itself.
has abstract
In the mathematical field of s ...... y, model theory, and topology.
@en
Wikipage page ID
67,416,519
page length (characters) of wiki page
Wikipage revision ID
1,025,136,482
Link from a Wikipage to another Wikipage
date
July 2016
@en
id
ultrafilter
@en
math statement
Every proper filter on a set is contained in some ultrafilter on
@en
If is an ultrafilter on then ...... as a subset.
is sequential.
@en
name
Proposition
@en
The ultrafilter lemma/principle/theorem
@en
reason
A function m can certainly be ...... . They should be stated here.
@en
title
Ultrafilter
@en
wikiPageUsesTemplate
type
comment
In the mathematical field of s ...... er (necessarily) being itself.
@en
label
Ultrafilter (set theory)
@en