Definition of Ultrafilters. Meaning of Ultrafilters. Synonyms of Ultrafilters

- and ultrafilters on P ( X ) {\displaystyle {\mathcal {P}}(X)} are usually called ultrafilters on the set X {\displaystyle X} . An ultrafilter on a set...
- {\displaystyle X\setminus A} belongs to the ultrafilter. Ultrafilters on sets are an important special instance of ultrafilters on partially ordered sets, where...
- set of all ultrafilters on X, with the elements of X corresponding to the prin****l ultrafilters. The topology on the set of ultrafilters, known as the...
- ultrafilter lemma implies that non-prin****l ultrafilters exist on every infinite set (these are called free ultrafilters). Every net valued in a singleton subset...
- equal almost everywhere as defined by an ultrafilter. The definition of almost everywhere in terms of ultrafilters is closely related to the definition in...
- sets that matter is given by any free ultrafilter U on the natural numbers; these can be characterized as ultrafilters that do not contain any finite sets...
- proving that certain perfect sets are uncountable, and the construction of ultrafilters. Let X {\textstyle X} be a set and A {\textstyle {\mathcal {A}}} a nonempty...
- a κ {\displaystyle \kappa } -complete ultrafilter. (W. W. Comfort, S. Negrepontis, The Theory of Ultrafilters, p.185) κ {\displaystyle \kappa } has Alexander's...
- characterizations of "ultrafilter" and "ultra prefilter," which are listed in the article on ultrafilters. Important properties of ultrafilters are also described...
- characterizations of "ultrafilter" and "ultra prefilter," which are listed in the article on ultrafilters. Important properties of ultrafilters are also described...