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Universal Fréchet sets in Banach spaces

By Michael J. Doré


We define a universal Fréchet set S of a Banach space Y as a subset containing a\ud point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a\ud sufficient condition for S to be a universal Fréchet set and use this to construct new\ud examples of such sets. The strongest such result says that in a non-zero Banach\ud space Y with separable dual one can find a universal Fréchet set S ⊆ Y that is\ud closed, bounded and has Hausdorff dimension one

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