# descending chain condition

A partially ordered set^{} $S$ (for example, a collection^{} of subsets of a set $X$, ordered by inclusion) satisfies the descending chain condition^{} or DCC if there does not exist an infinite descending chain ${s}_{1}>{s}_{2}>\mathrm{\cdots}$ of elements of $S$.

See also the ascending chain condition^{} (ACC).

Title | descending chain condition |
---|---|

Canonical name | DescendingChainCondition |

Date of creation | 2013-03-22 12:01:14 |

Last modified on | 2013-03-22 12:01:14 |

Owner | antizeus (11) |

Last modified by | antizeus (11) |

Numerical id | 7 |

Author | antizeus (11) |

Entry type | Definition |

Classification | msc 06A99 |

Synonym | DCC |