TY - JOUR
ID - 2199
TI - A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Khatami, Seyed M. A.
AD - Department of Computer Science, Birjand University of Technology, Birjand, Iran.
Y1 - 2022
PY - 2022
VL - 9
IS - 2
SP - 281
EP - 298
KW - BL-algebra
KW - dual of BL-algebra
KW - topological BL-algebra
DO - 10.22044/jas.2021.10296.1509
N2 - This 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.
UR - https://jas.shahroodut.ac.ir/article_2199.html
L1 - https://jas.shahroodut.ac.ir/article_2199_dfd241457e2e2e2e3a972fe61649d936.pdf
ER -