In this paper we present an extension of the Minkowski embedding theorem, showing the existence of an isometric embedding between the class F-c(H) of compact-convex and level-continuous fuzzy sets on a real separable Banach space H and L([0,1] x B(H*)), the Banach space of real continuous functions defined on the Cartesian product between [0,1] and the unit ball B(H*) in the dual space H*. Also, by using this embedding, we give some applications to the characterization of relatively compact subsets of F-c(H). In particular, an Ascoli-Arzela type theorem is proved and applied to solving the Cauchy problem (x)over dot (t) = f(t,x(t)), x(t(0)) = x(0) on F-c(H). (C) 2002 Elsevier Science Inc. All rights reserved.14441730227247