# meet

Certain posets $X$ have a binary operation^{} *meet* denoted by $\wedge $, such that $x\wedge y$ is the greatest lower bound^{} of $x$ and $y$. Such posets are called *meet-semilattices*, or *$\mathrm{\wedge}$-semilattices*, or *lower semilattices*.

If $m$ and ${m}^{\prime}$ are both meets of $x$ and $y$, then $m\le {m}^{\prime}$ and $m\ge {m}^{\prime}$, and so $m={m}^{\prime}$; thus a meet, if it exists, is unique. The meet is also known as the *and operator*.

Title | meet |

Canonical name | Meet |

Date of creation | 2013-03-22 12:27:37 |

Last modified on | 2013-03-22 12:27:37 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 10 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 06A12 |

Synonym | and operator |

Related topic | Join |

Related topic | Semilattice |

Defines | meet-semilattice |

Defines | meet semilattice |

Defines | lower semilattice |