Comparison of two topologies on IL-algebra

The main objective of this paper is to compare two linear topologies on IL-algebra. An open problem was proposed by Zahiri and Borzooei in 2016 in the context of topological BL-algebras, where they ask for necessary and sufficient conditions for two particular topologies to coincide. A partial solution to this problem in the case of topological IL-algebra is given. This study generalizes similar studies on topological FL _ ew -algebra, BL-algebra, and MV-algebra.