On the compactness and separability of E(X)

Let X be a metric space and E(X) the class of fuzzy compact sets on X, equiped with the generalized Hausdorff metric D which take the supremum on the Hausdorff distances between the corresponding /spl alpha/-level sets. The aim of this paper is, on the one hand, to analyze the compactness and separability of E(X) with respect to the compactness and separability of X, and on the other, to study these properties on the subclass E/sub c/(X) of level-continuous fuzzy sets.