Definition is_scott_continuous {X Y : hSet} (DX : dcpo_struct X) (DY : dcpo_struct Y) (f : X → Y) : UU := is_monotone DX DY f × (∀ (I : UU) (D : I → X) (HD : is_directed DX D) (x : X) (Hx : is_least_upperbound DX D x), is_least_upperbound DY (λ i, f(D i)) (f x)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness.