In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset.
An analogous definition applies to Knaster's condition downwards.
The property is named after Polish mathematician Bronisław Knaster.
Not unlike ccc, Knaster's condition is also sometimes used as a property of a topological space, in which case it means that the topology (as in, the family of all open sets) with inclusion satisfies the condition.
), ccc implies Knaster's condition, making the two equivalent.