On (Semi)Topological $BL$-algebras

In last ten years many mathematicians have studied prop- erties 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 relation- ships 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 BL- algebras and derive here conditions that imply a BL-algebra to be a semitopological or topological BL-algebra.