Topological properties of the class of generators of an indistinguishability operator (Q1826615)

The definition of a \(*\)-indistinguishability operator was given by \textit{L. Valverde} [Fuzzy Sets Syst. 17, 313--328 (1985; Zbl 0609.04002)]. The present article uses this concept to correlate the notion of classical topology with that of Lowen's fuzzy topology. Certain topologies and fuzzy topologies are also constructed. Consideration of such a fuzzy topology or a fuzzy co-topology (in Lowen's sense) in terms of the class of all generators of the \(*\)-indistinguishability operator (corresponding to a continuous t-norm \(*\)) can already be found in the literature. The author obtains an interesting result that, by use of a suitable \(*\)-indistinguishability operator, one can always construct a pseudometric which is topologically equivalent to the pseudometric of a classical pseudometrizable space.