(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce the definition of a hyper operation * on the set [0,1], and with this hyper operation, we will show that [0,1] is a hyper BCK-algebra. We also investigate the topologies that will be formulated with B_R([0,1]) and B_L([0,1]) and show some topology of R_[0,1](A) and L_[0,1](A). Furthermore, we investigate a basis for the intersection of topologies τ_R(H) and τ_L(H).