Dictionary

cofinality en · NOUN

Etymology

Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-lbor. English co- English final English cofinal Proto-Indo-European *-teh₂ Proto-Indo-European *-ts Proto-Indo-European *-teh₂ts Latin -itāsder. Old French -itebor. Middle English -ite English -ity English cofinality From cofinal + -ity.

Meanings

1. (countable) The least cardinality of a cofinal subset of a partially ordered set.
   • The cofinality of any set with a greatest element is 1.
   • 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. (uncountable) The property of being cofinal.

Forms

Relateds

cofinal · coinitial · coinitiality

Translations (2)

pl współkońcowość (the property of being cofinal) · es cofinalidad (the least of cardinalities of cofinal subsets)