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Universal Fréchet sets in Banach spaces
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Doré, Michael J. (2010) Universal Fréchet sets in Banach spaces. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2338614~S15
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Fréchet spaces, Banach spaces, Lipschitz spaces | ||||
Official Date: | March 2010 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Preiss, David | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) EP/D053099/1 ; University of Warwick | ||||
Extent: | iv, 88 leaves | ||||
Language: | eng |
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