Abstract: | A purely topological characterization of relatively compact sets is given for the metric space (K(Y),D) of upper semicontinuous, compact-supported, normal fuzzy subsets of a metric space Y. The considered metric D is that of the distance between fuzzy subsets, which is the supremum of the Hausdorff distances of the corresponding level sets. In the given proof the compactness of a variational convergence which was introduced by De Giorgi and Franzoni is fundamental. |