Category:Up-Complete Semilattices

This category contains results about up-complete semilattice.

Let $\left({S, \precsim}\right)$ be a preordered set.

Then $\left({S, \precsim}\right)$ is up-complete if and only if:

every directed subset of $S$ admits a supremum in $\left({S, \precsim}\right)$.