- 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...
-
equal almost everywhere as
defined by an
ultrafilter. The
definition of
almost everywhere in
terms of
ultrafilters is
closely related to the
definition in...
-
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...
- dual to a
filter is an
order ideal.
Special cases of
filters include ultrafilters,
which are
filters that
cannot be enlarged, and
describe nonconstructive...
- 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...
-
characterizations of "
ultrafilter" and "ultra prefilter,"
which are
listed in the
article on
ultrafilters.
Important properties of
ultrafilters are also described...
- a κ {\displaystyle \kappa } -complete
ultrafilter. (W. W. Comfort, S. Negrepontis, The
Theory of
Ultrafilters, p.185) κ {\displaystyle \kappa } has Alexander's...
-
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...
