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.
Highlights
Kim [1] introduced the concept of Balgebras in 2002. It is an algebraic system which is related to BCK/BCI-algebras but seems to have more profound properties without being excessively complicated
By the definition of Cartesian product topology, it follows that U × V is a nbd of (a, b)
We shall construct a B-topology on a Balgebra which is generated by a neighborhood base of the constant element, making the space a TB-algebra provided that the B-algebra is commutative
Summary
S. Kim [1] introduced the concept of Balgebras in 2002. Kim [1] introduced the concept of Balgebras in 2002 It is an algebraic system which is related to BCK/BCI-algebras but seems to have more profound properties without being excessively complicated. Certain properties and results on B-algebras were established via the properties of groups. The theory of topological groups is one of the already well-defined concepts in both algebra and topology. Some fundamental properties of a topological B-algebra that anchors on the basic topological and algebraic concepts will be investigated. This will provide the foundation of future investigations regarding the overall structure of a topological B-algebra
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