About: Ultrafilter on a set

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Maximal proper filter

Property	Value
dbo:description	maximal proper filter (en)
dbo:thumbnail	wiki-commons:Special:FilePath/Filter_vs_ultrafilter.svg?width=300
dbp:id	ultrafilter (en)
dbp:mathStatement	Every proper filter on a set is contained in some ultrafilter on (en) If is an ultrafilter on then the following are equivalent: is fixed, or equivalently, not free. is principal. Some element of is a finite set. Some element of is a singleton set. is principal at some point of which means for some does contain the Fréchet filter on as a subset. is sequential. (en)
dbp:name	Proposition (en) The /principle/theorem (en)
dbp:title	Ultrafilter (en)
dbp:wikiPageUsesTemplate	dbt:Set_theory dbt:Nlab dbt:Cite_book dbt:Reflist dbt:Math dbt:Anchor dbt:Cite_journal dbt:Sfn dbt:See_also dbt:Pi dbt:Citation dbt:About dbt:Bourbaki_General_Topology_Part_I_Chapters_1-4 dbt:Dugundji_Topology dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Schechter_Handbook_of_Analysis_and_Its_Foundations dbt:Citation_needed dbt:Visible_anchor dbt:Em dbt:Math_theorem dbt:Mathematical_logic dbt:Rp dbt:Vanchor dbt:Annotated_link dbt:Short_description dbt:Arkhangel'skii_Ponomarev_Fundamentals_of_General_Topology_Problems_and_Exercises dbt:Császár_General_Topology dbt:Dixmier_General_Topology dbt:Dolecki_Mynard_Convergence_Foundations_Of_Topology dbt:Joshi_Introduction_to_General_Topology dbt:Schubert_Topology
dct:subject	dbc:Families_of_sets dbc:Nonstandard_analysis dbc:Order_theory
rdf:type	owl:Thing
rdfs:label	Ultrafilter on a set (en)
rdfs:seeAlso	dbr:Filter_(mathematics) dbr:Boolean_prime_ideal_theorem
prov:wasDerivedFrom	wikipedia-en:Ultrafilter_on_a_set?oldid=1294127441&ns=0
foaf:depiction	wiki-commons:Special:FilePath/Filter_vs_ultrafilter.svg
foaf:isPrimaryTopicOf	wikipedia-en:Ultrafilter_on_a_set
is foaf:primaryTopic of	wikipedia-en:Ultrafilter_on_a_set