Open AccessTopobooleans and Boolean contact algebras with interpolation property
Author(s) -
Ali Akbar Estaji,
Toktam Haghdadi,
Javad Farokhi Ostad
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2109895e
Subject(s) - mathematics , injective function , property (philosophy) , iterated function , homomorphism , monomorphism , morphism , discrete mathematics , interpolation (computer graphics) , pure mathematics , function (biology) , combinatorics , image (mathematics) , mathematical analysis , computer science , artificial intelligence , philosophy , epistemology , evolutionary biology , biology
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 : B1 ? B2 is a complete Boolean homomorphism and (A,C) is an ICA, then B possesses a final ICA-structure in respect of f.