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 $s_1 > s_2 > \cdots$ of elements of $S$ .

See also the ascending chain condition (ACC).

descending chain condition is owned by anti zeus.

How to Cite This Entry

anti zeus. "descending chain condition" (version 3). PlanetMath.org. Freely available at http://planetmath.org/DescendingChainCondition.html.

Classification

AMS MSC:

06A99 (Order, lattices, ordered algebraic structures :: Ordered sets :: Miscellaneous)

Pending Errata and Addenda

None. [ View all 4 ]

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