Definition. Directed-complete partial order (DCPO) [math-XL3D]

A poset DD is complete if every directed subset P⊆DP \subseteq D has a least upper bound.

Example Every discrete poset is a DCPO [math-4J1T]

Every discrete poset (A,=)(A, =) is a DCPO, every singleton sets ∀x∈A,{x}\forall x \in A, \{ x \} are directed, with least upper bound xx.

Definition Category of DCPOs [math-P5X4]