View source for Cofinal set

{{TEX|done}}{{MSC|06A}}

''in a [[partially ordered set]] $(A,{<})$''

A subset $B$ of $(A,{<})$ with the property that for every $a \in A$ there is $b \in B$ such that $a \le b$.  Dually, a ''co-initial set'' $B$ has the property that for every $a \in A$ there is $b \in B$ such that $b \le a$.

====References====
* R. Fraïssé, ''Theory of Relations'', Studies in Logic and the Foundations of Mathematics, Elsevier (2011) p.44. {{ISBN|0080960413}}