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 \mathcal{L}=(L, \wedge, \vee, *, \too , ۰, ۱), 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 [۰,۱] 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.

Keywords:

BL-algebra , dual of BL-algebra , topological BL-algebra