ultrafilter (Q1571831)

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maximal proper filter
  • maximal filter
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Language Label Description Also known as
English
ultrafilter
maximal proper filter
  • maximal filter

Statements

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Filter vs ultrafilter.svg
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in the powerset lattice of {1,2,3,4}, the principal filter ↑{1,4} (dark green) isn’t an ultrafilter since it can be extended to the larger nontrivial filter ↑{1} by including also the light green elements; but ↑{1} is an ultrafilter since it can’t be so extended (English)
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