Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
ultrafilter
|
| gptkbp:cardinality |
2^2^|X| on set X
|
| gptkbp:contrastsWith |
gptkb:principal_ultrafilter
|
| gptkbp:definedIn |
gptkb:box_set
|
| gptkbp:does_not_exist_on |
finite set
|
| gptkbp:exists_on |
infinite set
|
| gptkbp:field |
gptkb:mathematics
gptkb:set_theory gptkb:topology |
| gptkbp:heldBy |
ultrafilter that is not principal
|
| https://www.w3.org/2000/01/rdf-schema#label |
free ultrafilter
|
| gptkbp:property |
contains no finite set
every cofinite set is in the ultrafilter not generated by a single element |
| gptkbp:relatedTo |
gptkb:Zorn's_lemma
axiom of choice |
| gptkbp:used_in |
gptkb:Stone–Čech_compactification
gptkb:nonstandard_analysis model theory ultraproduct construction |
| gptkbp:bfsParent |
gptkb:Ramsey_ultrafilter
|
| gptkbp:bfsLayer |
6
|