Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak * denting points norm dense in the unit sphere. A characterisation of Banach spaces whose duals have a corresponding intersection property is established. The question of the density of the strongly exposed points of the ball is examined for spaces with such properties. It was Mazur [7] who drew attention to the euclidean space property (I): every bounded closed convex set can be represented as an intersection of closed balls; and he began the investigation to determine those normed linear spaces which possess this property. Phelps [9] continued this investigation, characterising finite dimensional spaces with property (I). Recently, Sullivan [/2] has given a characterisation of smooth spaces with property (I).
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