Lowen, para-Lowen, and \(\alpha\)-level functors and fuzzy topologies on the crisp real line (Q1105218)

The author extends Lowen's \(\omega\)-construction for nonlinear lattices and generalizes the notion of topological fuzzy topologies. In this context there exist non-topological fuzzy topologies on \({\mathbb{R}}\) which are Hutton-Erceg metrizable [\textit{M. A. Erceg}, J. Math. Anal. Appl. 69, 205-230 (1979; Zbl 0409.54007)]. In these examples the Erceg metric is strongly \(\alpha\)-complete for each \(\alpha\) and agrees with the Euclidean metric on singletons. The examples occur in the class of fuzzy co-duals constructed by the author in the paper reviewed in Zbl 0648.54005.