Analyzing Some Structural Properties of Topological B-Algebras

Abstract

In this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B-topology, making a TB-algebra in which the filterbase is a neighborhood base of the constant element, provided that the given B-algebra is commutative. Finally, we investigate subalgebras of TB-algebras and introduce the notion of quotient TB-algebras of the given B-algebra.

On bi-topological BCK-algebras

“…In 1999 Jun et al [9] introduced topological BCI-algebras, provided some properties of this structure, and characterized a topological BCI-algebra in terms of neighborhoods. Gonzaga [6] in 2019, introduced the concept of a topological B-algebra which characterized a topological B-algebra concerning open sets.…”

On B-ideals in a Topological B-Algebra

“…Definition 2. [6] Let A and B be nonempty subsets of a B-algebra X. The product of A and B, denoted by A * B, is given by…”

“…Theorem 2. [6] Let X = (X, * , 0) be a B-algebra and τ a B-topology on the set X. Then (X, τ ) is a topological B-algebra if and only if for all x, y in X and for every neighborhood W of x * y, there are neighborhoods U and V of x and y, respectively, such that U * V ⊆ W .…”