Affiliation:
1. Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran
2. Department of Basic Sciences, Birjand University of Technology, Birjand, Iran
Abstract
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.
Publisher
National Library of Serbia