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Keywords:
Urysohn's universal space; ultrahomogeneous spaces; functor; extensions of isometries
Urysohn's universal space; ultrahomogeneous spaces; functor; extensions of isometries
Summary:
The aim of the paper is to prove that in the unbounded Urysohn universal space $\mathbb U$ there is a functor of extension of $\Lambda $-isometric maps (i.e. dilations) between central subsets of $\mathbb U$ to $\Lambda $-isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group $\mathbb R \setminus \{0\}$ acts continuously on $\mathbb U$ by $\Lambda $-isometries.
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