Topologies on Hyper BCK-Algebra \([0, 1]\)

In this paper, we introduce the definition of a hyper operation $\ast$ 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 $\tau_{R}(H)$ and $\tau_{L}(H)$.