Interior and closure operators on bounded commutative residuated ℓ-monoids

Abstract

Topological Boolean algebras are generalizations of topological spaces dened by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Lukasiewicz innite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative R‘-monoids that contains e.g. the classes of BL-algebras (i.e., algebras of the H ajek’s basic fuzzy logic) and Heyting algebras as proper subclasses.