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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, T B -algebras) and some properties are investigated. A characterization of T B -algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B -topology, making a T B -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 T B -algebras and introduce the notion of quotient T B -algebras of the given B -algebra.

Analyzing Some Structural Properties of Topological B -Algebras