Definition of Ultrafilter. Meaning of Ultrafilter. Synonyms of Ultrafilter

Here you will find one or more explanations in English for the word Ultrafilter. Also in the bottom left of the page several parts of wikipedia pages related to the word Ultrafilter and, of course, Ultrafilter synonyms and on the right images related to the word Ultrafilter.

Definition of Ultrafilter

No result for Ultrafilter. Showing similar results...

Meaning of Ultrafilter from wikipedia

- In the mathematical field of order theory, an ultrafilter on a given partially ordered set (or "poset") P {\textstyle P} is a certain subset of P , {\displaystyle...
- In the mathematical field of set theory, an ultrafilter on a set X {\displaystyle X} is a maximal filter on the set X . {\displaystyle X.} In other words...
- property true almost everywhere is sometimes defined in terms of an ultrafilter. An ultrafilter on a set X is a maximal collection F of subsets of X such that:...
- ideals. A variation of this statement for filters on sets is known as the ultrafilter lemma. Other theorems are obtained by considering different mathematical...
- prin****l ultrafilter on X {\displaystyle X} . Moreover, every prin****l ultrafilter on X {\displaystyle X} is necessarily of this form. The ultrafilter lemma...
- be extended to an ultrafilter, but the proof uses the axiom of choice. The existence of a nontrivial ultrafilter (the ultrafilter lemma) can be added...
- ultrafilter is called the ultrafilter lemma and cannot be proven in Zermelo–Fraenkel set theory (ZF), if ZF is consistent. Within ZF, the ultrafilter...
- former is equivalent in ZF to Tarski's 1930 ultrafilter lemma: every filter is a subset of some ultrafilter. One of the most interesting aspects of the...
- to the following criterion: ****uming the ultrafilter lemma, a space is compact if and only if each ultrafilter on the space converges. With this in hand...
- characterizations of "ultrafilter" and "ultra prefilter," which are listed in the article on ultrafilters. Important properties of ultrafilters are also described...