A chain condition on a partially ordered set is a condition that requires sequences in to become eventually constant. The condition that all increasing sequences in become eventually constant is called the increasing chain condition, while the dual condition that all decreasing sequences in become eventually constant is called the decreasing chain condition.

# Chain Condition

## See also

Ascending Chain Condition, Descending Chain Condition## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Chain Condition."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ChainCondition.html