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Title: Universal Fréchet sets in Banach spaces
Author: Doré, Michael J.
ISNI:       0000 0004 2697 5519
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2010
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We define a universal Fréchet set S of a Banach space Y as a subset containing a point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a sufficient condition for S to be a universal Fréchet set and use this to construct new examples of such sets. The strongest such result says that in a non-zero Banach space Y with separable dual one can find a universal Fréchet set S ⊆ Y that is closed, bounded and has Hausdorff dimension one.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC) EP/D053099/1 ; University of Warwick
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics