Heyting* algebras, topological Boolean algebras and P.O. systems (Q1102308)

The background to this paper is the theory of topological Boolean algebras (TBA's) developed by R. S. Pierce. TBA's are closure algebras with a unary operation which captures algebraic properties of the Cantor-Bendixson derivation. Using the notion of Heyting algebras with a unary operation, also destined to capture algebraic properties of topological derivation, the author generalizes Pierce's duality to the category P of all partially ordered systems and morphisms of p.o. systems (as defined by Pierce) and to a category A of TBA's with some conditions.