# Cofinal set

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 $b \le a$.