# 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 |
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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 |