Topobooleans and Boolean contact algebras with interpolation property

Ali Akbar Estaji, Toktam Haghdadi, Javad Farokhi Ostad

In this paper we study the connections between topobooleans [A. A. Estaji, A. Karimi Feizabadi, and M. Zarghani, Categ. Gen. Algebr. Struct. Appl. 4 (2016), 75–94] and Boolean contact algebras with the interpolation property (briefly, ICAs) [G. Dimov and D. Vakarelov, Fund. Inform. 74 (2006), 209–249]. We prove that every complete ICA generates a topoboolean and, conversely, if a topoboolean satisfies some natural conditions then it generates a complete ICA which, in turn, generates it. We introduce the category ICA of ICAs and suitable morphisms between them. We show that the category ICA has products and every ICA-monomorphism is an injective function. We prove as well that if A and B are complete Boolean algebras, f : B 1 → B 2 is a complete Boolean homomorphism and (A, C) is an ICA, then B possesses a final ICA-structure in respect of f