Continuous poset
= Continuous poset
{title2=$x=\sup\{y:y\ll x\}$}
{wiki}
= Continuous partially ordered set
{synonym}
A <partially ordered set> in which, for every $x$, the elements <way-below> $x$ form a <directed set> with <least upper bound> $x$. Directed <least upper bounds> other than these approximating ones need not exist.