On the Boolean algebra induced by a unital \(\ell \)-group

The main goal of this paper is the study of the Boolean algebra of all characteristic elements in a unital \(\ell \) $\ell$ -group and we investigate some topological properties of it in the case that the unital \(\ell \) $\ell$ -group equipped with a link or positive filter topology. We also introduce the concept of Boolean region as a subset of a unital \(\ell \) $\ell$ -group.