document: Embedding of level-continuous fuzzy sets on Banach spaces In this paper we present an extension of the Minkowski embedding theorem , showing the existence of an isometric embedding between the classF/sub c / -LRB- X -RRB- of compact-convex and level-continuous fuzzy sets on a real separable Banach space X and C -LRB- -LSB- 0 , 1 -RSB- * B -LRB- X * -RRB- -RRB- , the Banach space of real continuous functions defined on the cartesian product between -LSB- 0 , 1 -RSB- and the unit ball B -LRB- X * -RRB- in the dual space X * . Also , by using this embedding , we give some applications to the characterization of relatively compact subsets of F/sub c / -LRB- X -RRB- . In particular , an Ascoli-Arzela type theorem is proved and applied to solving the Cauchy problem x -LRB- t -RRB- = f -LRB- t , x -LRB- t -RRB- -RRB- , x -LRB- t/sub 0 / -RRB- = x/sub 0 / on F/sub c / -LRB- X -RRB-
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