alternative characterization of filter

A collection $𝐅$ of subsets of a set $X$ is a filter if and only if the following condition is satisfied: For any two subsets $A$ and $B$ of $X$, it is the case that $A\cap B\in 𝐅$ if and only if $A\in 𝐅$ and $B\in 𝐅$.

Title	alternative characterization of filter
Canonical name	AlternativeCharacterizationOfFilter
Date of creation	2013-03-22 14:43:02
Last modified on	2013-03-22 14:43:02
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	5
Author	rspuzio (6075)
Entry type	Theorem
Classification	msc 03E99
Classification	msc 54A99