A. B. Khalaf - Department of Mathematics, University of Duhok, Duhok , Iraq
Nehmat Ahmed - Department of Mathematics, College of Education, Salahaddin University, Erbil, Iraq

The concept of pre-open set in topological spaces was introduced by Mashhour \cite{ma} and the concept of BCK-algebras was defined by Iseki \cite{ise}. The aim of this paper is to supply the BCK-algebra by a topology that makes the operation defined 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 defined in \cite{dong}. By using properties of pre-open sets and axioms of BCK-algebras, several topological properties on BCK-algebras are found.

T_i spaces (i=۰, ۱,۲), algebras, continuity