Analyzing some structural properties of topological \(B\)-algebras (Q2292326)

Summary: 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.