Notes on topological BL-algebras

In this study, we aim to solve the open problem posed by Zahiri and Borzooei [23], i.e., given an arbitrary linear topological BL-algebra (L,U), under what condition does its topology U coincides with the new one V induced by a system of filters. We investigate this problem for both finite BL-algebras and infinite BL-algebras. In the finite case, we give a necessary and sufficient condition. In the infinite case, we consider the conditions where the original topology U is zero-dimensional and (L,V) is an l-BL-algebra, respectively. In addition, we modify some examples of topological BL-algebras mentioned by Borzooei et al.