Abstract

In this paper we present an extension of the Minkowski embedding theorem, showing the existence of an isometric embedding between the class ?c(script x sign) of compact-convex and level-continuous fuzzy sets on a real separable Banach space (script x sign) and script c sign([0,1] × B(script x sign*)), the Banach space of real continuous functions defined on the cartesian product between [0,1] and the unit ball B(script x sign*) in the dual space script x sign*. Also, by using this embedding, we give some applications to the characterization of relatively compact subsets of ?c(script x sign). In particular, an Ascoli-Arzelá type theorem is proved and applied to solving the Cauchy problem ?(t) = f(t,x(t)), x(t0) = x0 on ?c(script x sign). © 2002 Elsevier Science Inc. All rights reserved.