cofinality

plural cofinalities

1. countablemathematicsThe least cardinality of a cofinal subset of a partially ordered set.

   The cofinality of any set with a greatest element is 1.

   1 more example

   The dual notion of cofinality is coinitiality: a set S#92;subseteqP is called coinitial if for every p#92;inP there is q#92;inS such that q#92;lep. Equivalently, a coinitial set in P is a cofinal set in P#92;ast#58;#61;(P,#92;ge). […] Both cofinality and coinitiality need not be well-defined for an arbitrary partial order (e.g. if the partial order is only made of two incomparable elements).

   2024 November 12, Steffen Lempp, Alberto Marcone, Manlio Valenti, “Chains and antichains in the Weihrauch lattice”, in arXiv, page 1, archived from the original on 23 Jun 2026

2. uncountablemathematicsThe property of being cofinal.