When is a fuzzy topology topological? (Q1089946)

\textit{R. Lowen} [Topology Appl. 12, 65-74 (1981; Zbl 0437.54004)] defined topological fuzzy topologies (intuitively, fuzzy topologies that are not significantly fuzzy). He also proved that compact, Hausdorff fuzzy topologies must be topological. We describe Lowen's concept using semi- closure operators and the hypergraph functor. The two main results are: (1) The \(\alpha\)-closure operators defined by a topological fuzzy topology are all identical and must be closure operators. (2) A fuzzy topology is topological if and only if the image under the hypergraph functor is a certain topological product.