(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The primary aim of this paper is applying the concept of b-open sets in topological spaces to explore the idea of b-topological d- algebra (Tbd-algebra), which is a d-algebra equipped with a specific type of topology that ensured the binary operation that is defined on them to be d-topologically continuous. This idea generalizes the notion of topological d-algebras. In addition, we present some relations between open sets and b-open sets in a Tbd-algebra. We also construct some relations between Ti and b-Ti-spaces for (i=0,1,2). Finally, we use left maps on positive implicative d-algebras to establish some Tbd-algebras.