My talk is based on article [1]. Our aim is to give a unified topological approach to several results about a certain type of fuzzy measures, namely T∞−valuations (2) on clans of fuzzy sets (1) (in the sense of Butnariu and Klement [2]). We will transfer the method of [3], used to study FN-topologies (4) and measures on Boolean rings, to the study of T∞−valuations. So we need, for the domain of...

The variety of MV-algebras is the equivalent algebraic semantics of the infinitely-valued Lukasiewicz logic [1], and MVn-algebras are algebraic models of the Lukasiewicz logic with n truth values (2 ≤ n < ω). Recall that an algebra A ∈ V is said to be a free algebra in a variety V, if there exists a set A0 ⊂ A such that A0 generates A and every mapping f from A0 to any algebra B ∈ V can be exte...