# Zermelo’s postulate

If $\mathcal{F}$ is a disjoint family of nonempty sets, then there is a set $C$ which has exactly one element of each $A\in \mathcal{F}$ (i.e such that $A\cap C$ is a singleton for each $A\in \mathcal{F}$.)

This is one of the many propositions^{} that are equivalent^{} to the axiom of choice^{}.

Title | Zermelo’s postulate^{} |
---|---|

Canonical name | ZermelosPostulate |

Date of creation | 2013-03-22 13:13:36 |

Last modified on | 2013-03-22 13:13:36 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 03E25 |

Related topic | AxiomOfChoice |

Related topic | MaximalityPrinciple |

Related topic | TukeysLemma |

Related topic | ZornsLemma |

Related topic | KuratowskisLemma |