# closed sublattice

A sublattice $K$ of a complete lattice^{} $L$ is a *closed sublattice* of $L$ iff $K$ contains the meet and the join of any its nonempty subset.

Examples:

Any complete^{} sublattice is a closed sublattice.

$[0;1]$ is a closed sublattice of $(-\mathrm{\infty};\mathrm{\infty})$.

The set of rational numbers is not a closed sublattice of the set of real numbers.

Title | closed sublattice |
---|---|

Canonical name | ClosedSublattice |

Date of creation | 2013-03-22 18:57:28 |

Last modified on | 2013-03-22 18:57:28 |

Owner | porton (9363) |

Last modified by | porton (9363) |

Numerical id | 5 |

Author | porton (9363) |

Entry type | Definition |

Classification | msc 06B23 |

Related topic | Sublattice |

Related topic | Lattice |