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

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.


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)
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