Ultrafilter
Definition, Meaning & Examples
Part of speech noun
Quick meaning: Ultrafilter is a noun meaning A device that performs ultrafiltration.
Meaning
A device that performs ultrafiltration.
More Meanings
- (mathematics, of a set, whose subsets are partially ordered by inclusion) A proper filter which has a law of dichotomy for complements.
- (mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.
- (transitive) To filter by ultrafiltration.
Example Sentences
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.
Word Forms
- ultrafilters
- ultrafiltering
- ultrafiltered
Related Words
Related dictionary entries include ultrafiltrate, electroultrafiltration, electro-ultrafiltration, ultradiafiltration, ultrainfiltration, electrofilter.
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Sources & Attribution
FreeDictionaryAPI.com / Wiktionary · Original source · CC BY-SA 4.0
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