Definition:Up-Complete

Definition

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 $\left({S, \precsim}\right)$.

Sources

• 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices

• Mizar article WAYBEL_0:def 39