Abstract
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 ϰ -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.
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