Geodesic
A note on Lipschitz isomorphisms in Hilbert spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 427-430.

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We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?
Classification : 46B03
Keywords: Lipschitz isomorphism; Hilbert space 
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     title = {A note on {Lipschitz} isomorphisms in {Hilbert} spaces},
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Ives, Dean. A note on Lipschitz isomorphisms in Hilbert spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 427-430. http://geodesic.mathdoc.fr/item/CMUC_2010__51_3_a3/