University of Guilan Journal of Algebra and Related Topics 2345-3931 11 1 2023 06 01 On pre-topological BCK-algebras 65 80 6796 10.22124/jart.2023.22990.1439 EN A. B. Khalaf Department of Mathematics, University of Duhok, Duhok , Iraq Nehmat Ahmed Department of Mathematics, College of Education, Salahaddin University, Erbil, Iraq Journal Article 2022 09 26 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 ($i=0, 1,2)$ algebras continuity https://jart.guilan.ac.ir/article_6796_4786aef61868aef537e77325b29183ee.pdf