fact: Definition compact_approximating_family (x : X) : directed_set X := pr1 (AX x).
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Basis.Continuous