Topologies on Hyper BCK-Algebra \([0, 1]\) (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 $τ_{L}(H)$.
Keywords: Hyper BCK-algebra, hyper order, bases, hyperoperation, topology