Definition scott_open_set_union {D : dcpo} {I : UU} (P : I → scott_open_set D) : scott_open_set D. Proof. use make_scott_open_set. - exact (⋃ P). - exact (is_scott_open_union P). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous.