Definition make_TopologicalSpace (X : hSet) (O : (X → hProp) → hProp) (is : isSetOfOpen_union O) (is0 : isSetOfOpen_htrue O) (is1 : isSetOfOpen_and O) : TopologicalSpace := (X,,O,,is,,(isSetOfOpen_finite_intersection_carac _ is0 is1)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.DivisionRig. Require Import UniMath.Algebra.ConstructiveStructures. Section TopologyFromNeighborhood. End TopologyFromNeighborhood. Definition TopologyFromNeighborhood {X : hSet} Lemma TopologyFromNeighborhood_correct {X : hSet} N x P <-> neighborhood (T := TopologyFromNeighborhood N H) x P. simple refine (TopologyFromNeighborhood _ _). apply TopologyFromNeighborhood_correct. simple refine (TopologyFromNeighborhood _ _). apply TopologyFromNeighborhood_correct. simple refine (TopologyFromNeighborhood _ _).