Representation Theorem for Heyting Lattices

The articles [11], [7], [13], [1], [14], [5], [6], [4], [9], [10], [15], [16], [12], [2], [3], and [8] provide the notation and terminology for this paper. Let us note that every lower bound lattice which is Heyting is also implicative and every lattice which is implicative is also upper-bounded. In the sequel T denotes a topological space and A, B denote subsets of the carrier of T . The following propositions are true: (1) A∩ Int(Ac∪B)⊆ B. (2) For every subset C of T such that C is open and A∩C ⊆ B holds C ⊆ Int(Ac∪B). Let T be a topological structure. The functor Topology(T ) yields a family of subsets of T and is defined as follows: (Def. 1) Topology(T ) = the topology of T . Let us consider T . One can check that Topology(T ) is non empty. The following proposition is true