Characteristic values of T-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 T-filters and T-filter bases (cf. [Hohle, 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 kappa-condition and consequently to give an alternative but equivalent definition of T-filters and T-filter bases. Some important properties of the characteristic value are also studied, which allows us to establish a relation between T-filters and both L-filters and L-filters of ordinary subsets. (c) 2005 Elsevier B.V. All rights reserved.
characteristic value t-filter characteristic set prefilter l-filter complete mv-algebra saturation