Shahrood University of TechnologyJournal of Algebraic Systems2345-51289220220101A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS281298219910.22044/jas.2021.10296.1509ENSeyed M. A.KhatamiDepartment of Computer Science, Birjand University of Technology, Birjand, Iran.Journal Article20201122This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra $\mathcal{L}=(L, \wedge, \vee, *, \too , 0, 1)$, the introduced topology is defined by a distance-like function between elements of $L$ which is defined by $a \leftrightarrow b=(a\too b)*(b\too a)$. We will show that when the continuous scale $[0,1]$ is endowed to be a BL-algebra, then this topology admits some of the most important properties of the metric topology. Finally, we will show that this topology can be examined by a similar topology on dual of BL-algebras as well.https://jas.shahroodut.ac.ir/article_2199_dfd241457e2e2e2e3a972fe61649d936.pdf