On (Semi)Topological BL-algebras

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean [5] studied compact representations of BL-algebras, L. C. Ciungu [4] investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim [13] studied relationships between closure operators and BL-algebras, M.Haveshki, E. Eslami and A. Broumand Saeid [9] applied filters to construct a topology on BL-algebras.In this paper we define semitopological and topological BLalgebras and derive here conditions that imply a BL-algebra to be a semitopological or topological BL-algebra.