2 00 5 Extension theorems and reconstruction theorems for the Urysohn Universal Space
نویسنده
چکیده
Such a space is unique up to isometry. We shall investigate group LIP(U) of bilipschitz homeomorphisms of U and some related groups. Indeed, the group H(U) of all homeomorphisms of U comes to mind first. However, by V. Uspenskiy [Us], U is homeomorphic to l2. So H(U) is in fact the group of homeomomorphisms of a Banach space, and can be better understood as such. For LIP(U) and for other groups defined via the metric of U, the fact that U ∼= l2 does not seem to help. The main tool and also the main result in this work is an extension theorem for finite bilipschitz functions defined on subsets of U (Theorem 2.1). Suppose that A is a finite subset of U and f : A → U is K-bilipschitz. We
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Extension and reconstruction theorems for the Urysohn universal metric space
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