Topologies on a Hyper Sum and Hyper Product of Two Hyper BCK-algebras

Abstract

Given a hyper BCK-algebra (H, ∗, 0), each of the families BL(H) = {LH(A) : ∅ 6=
A ⊆ H} and BR(H) = {RH(A) : ∅ 6= A ⊆ H} forms a base for some topology on H, where LH(A) = {x ∈ H : x a, ∀a ∈ A} and RH(A) = {x ∈ H : a x, ∀a ∈ A} for any subset A of H. In this paper, we determine the bases of the topologies induced by the hyper sum H1 ⊕ H2 and hyper product H1 × H2, where (H1, ∗1, 01) and (H2, ∗2, 02) are two hyper BCK-algebras.