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bn:02546747n
Noun Concept
Categories: Order theory, Non-standard analysis
EN
ultrafilter  Fixed ultrafilter  Free ultrafilter  Trivial ultrafilter  Ultra filter
EN
In the mathematical field of order theory, an ultrafilter on a given partially ordered set P {\textstyle P} is a certain subset of P, {\displaystyle P,} namely a maximal filter on P ; {\displaystyle P;} that is, a proper filter on P {\textstyle P} that cannot be enlarged to a bigger proper filter on P. Wikipedia
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EN
In the mathematical field of order theory, an ultrafilter on a given partially ordered set P {\textstyle P} is a certain subset of P, {\displaystyle P,} namely a maximal filter on P ; {\displaystyle P;} that is, a proper filter on P {\textstyle P} that cannot be enlarged to a bigger proper filter on P. Wikipedia
Maximal proper filter Wikidata
A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter. Wiktionary
EN
An ultrafilter is maximal in the sense that if any other element of the poset not already in it were added to it, one could deduce (from the laws which define the filter, and the given ordering relation, i.e., the structure of the poset) that the resulting filter must be improper; i.e., it must contain all the elements of the poset. Wiktionary
IS A
filter
PART OF
extender
Wikipedia
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ultrafilter
Wikidata
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ultrafilter
Wiktionary
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ultrafilter
Wikipedia Redirections
EN
Fixed ultrafilter, Free ultrafilter, Trivial ultrafilter, Ultra filter

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