# alternative characterization of filter

A collection $\mathbf{F}$ 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 $A\cap B\in\mathbf{F}$ if and only if $A\in\mathbf{F}$ and $B\in\mathbf{F}$.

Title alternative characterization of filter AlternativeCharacterizationOfFilter 2013-03-22 14:43:02 2013-03-22 14:43:02 rspuzio (6075) rspuzio (6075) 5 rspuzio (6075) Theorem msc 03E99 msc 54A99