Semitopological BL-Algebras and MV -Algebras

Abstract

Abstract. In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology τx 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 M V -algebra by using two kinds of definition of M V -algebra and show that they are equivalent. IntroductionIn [13], Hájek proposed his logic BL as a common fragment of all traditional many valued logics (Łukasiewicz, Gödel and Product Logics). In [16], BL has been proved to be complete with respect to a variety of algebras called BL-algebras. BL-algebras are the algebraic structure for Hájek's Basic Logic. M V -algebras, Gödel algebras and Product algebras are the most known classes of BL-algebras. In the last 10 years, many mathematicians have studied the properties of BL-algebras endowed with a topology. 2010 Mathematics Subject Classification: 03G25, 54E15, 54H99.