In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology T x on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of MV -algebra and show that they are equivalent.
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