# join

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

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

Title | join |

Canonical name | Join |

Date of creation | 2013-03-22 12:27:40 |

Last modified on | 2013-03-22 12:27:40 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 11 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 06A12 |

Synonym | or operator |

Related topic | Meet |

Related topic | Semilattice |

Defines | join-semilattice |

Defines | join semilattice |

Defines | upper semilattice |