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), the introduced topology is defined by a distance-like function between elements of l which is defined by a↔b=(atoob)∗(btooa). 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.