Characteristic values of ⊤-filters

In this paper we extend the notions of characteristic set and characteristic value of a prefilter (cf. [Lowen, Convergence in fuzzy topological spaces, Gen. Topol. Appl. 10 (1979) 147-160]) to the setting of ⊤-filters and ⊤-filter bases (cf. [Höhle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Math. 38 (1982) 289-323]) in the lattice valued context of complete MV-algebras. This notion allows us to reinterpret the Ï°-condition and consequently to give an alternative but equivalent definition of ⊤-filters and ⊤-filter bases. Some important properties of the characteristic value are also studied, which allows us to establish a relation between ⊤-filters and both L-filters and L-filters of ordinary subsets.