MMN-1803
Quasi-semi-homomorphisms and generalized proximity relations between Boolean algebras
Sergio A. Celani;Abstract
In this paper we shall introduce the notion of quasi-semi-homomorphisms
between Boolean algebras, as a generalization of the quasi-modal operators
introduced in \cite{Celani}, of the notion of meet-homomorphism studied
in \cite{Halmos} and \cite{Graf}, and the notion of precontact or
proximity relation defined in \cite{D=0000FCntsch-Vakarelov2007}.
We will prove that the class of Boolean algebras with quasi-semi-homomorphism
is a category, denoted by $\mathbf{BoQS}$. We shall prove that this
category is equivalent to the category $\mathbf{StQB}$ of Stone spaces
where the morphisms are binary relations, called quasi-Boolean relations,
satisfying additional conditions. This duality extends the duality
for meet-homomorphism given by P. R. Halmos in \cite{Halmos} and
the duality for quasi-modal operators proved in \cite{Celani}.
Vol. 19 (2018), No. 1, pp. 171-189
DOI: 10.18514/MMN.2018.1803