coinitiality 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- Proto-Indo-European *h₁én Proto-Italic *en Proto-Italic *en- Proto-Indo-European *h₁ey- Proto-Indo-European *h₁éyti Proto-Italic *ejō Proto-Italic *eō Proto-Italic *eneō Latin ineō Proto-Indo-European *-(i)yós Proto-Italic *-ijos Proto-Italic *-ios Old Latin -ios Latin -iusnom. Latin -ium Latin initium Proto-Indo-European *h₂el- Proto-Indo-European *-is Proto-Indo-European *h₂élisder.? Proto-Italic *-ālis Latin -ālis Latin initiālislbor. Middle French initialbor. ▲ Latin initiālislbor. English initial English coinitial Proto-Indo-European *-teh₂ Proto-Indo-European *-ts Proto-Indo-European *-teh₂ts Latin -itāsder. Old French -itebor. Middle English -ite English -ity English coinitiality From coinitial + -ity.
Meanings
- (countable) The least cardinality of a coinitial subset of a partially ordered set.
-
(uncountable) The property of being coinitial.
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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| coinitialities | Number=Plur | lexicographic |