A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS

This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra L=(L,∧,∨,∗,\too,0,1)L=(L,∧,∨,∗,\too,0,1), the introduced topology is defined by a distance-like function between elements of LL which is defined by a↔b=(a\toob)∗(b\tooa)a↔b=(a\toob)∗(b\tooa). We will show that when the continuous scale [0,1][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.