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What does ultrafilter mean?

Looking for the meaning or definition of the word ultrafilter? Here's what it means.

Noun
  1. (mathematics) A proper filter which has a law of dichotomy for complements.
  2. (mathematics) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.
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Examples
The nexine is an ultrafilter membrane, which is impermeable to most proteins.
The polymers at first were concentrated inside the wall, which acted as an ultrafilter.

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