On pre-topological BCK-algebras

TThe concept of pre-open set in topological spaces was introduced by Mashhour [13] and the concept of BCK-algebras was defined by Iseki [9]. The aim of this paper is to supply the BCK-algebra by a topology that makes the operation de ned on X satisfy a special type of continuity with help of pre-open sets we call it p-topological BCK-algebra. This concept is an extension of the concept of topological BCK-algebra which was de ned in [12]. By using properties of pre-open sets and axioms of BCK-algebras, several topological properties on BCK-algebras are found.