In order theory, a partially ordered set X is said to satisfy the countable chain condition, or to be ccc, if every strong antichain in X is countable.
The countable chain condition means the downwards countable chain condition, in other words no two elements have a common lower bound.
For example, if κ is a cardinal, then in a complete Boolean algebra every antichain has size less than κ if and only if there is no descending κ-sequence of elements, so chain conditions are equivalent to antichain conditions.
Partial orders and spaces satisfying the ccc are used in the statement of Martin's axiom.
A topological space is said to satisfy the countable chain condition, or Suslin's Condition, if the partially ordered set of non-empty open subsets of X satisfies the countable chain condition, i.e. every pairwise disjoint collection of non-empty open subsets of X is countable.