Directed-complete partial order
= Directed-complete partial order
{title2=$\bigvee D$}
= Directed-complete
{synonym}
A <partially ordered set> is directed-complete if every <directed set> in it has a <least upper bound>. A <complete lattice> is directed-complete. Conversely, directed completeness together with all finite <joins>, including the empty join, gives arbitrary <joins>: take the <directed set> of joins of finite subsets.