Extension and reconstruction theorems for the Urysohn universal metric space. (English) Zbl 1224.22010

Kubiś, Wiesław; Rubin, Matatyahu

Czech. Math. J. 60, No. 1, 1-29 (2010).

Summary: We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

MSC:

22F50	Groups as automorphisms of other structures
54E40	Special maps on metric spaces
51F99	Metric geometry
20E36	Automorphisms of infinite groups
54H11	Topological groups (topological aspects)

Keywords:

Urysohn space; bi-Lipschitz homeomorphism; modulus of continuity; reconstruction theorem; extension theorem

References:

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