## Piotr Niemiec

*Functor of extension of $\Lambda$-isometric maps between central subsets of the unbounded Urysohn universal space*

Comment.Math.Univ.Carolin. 51,3 (2010) 541-549.**Abstract:**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.

**Keywords:** Urysohn's universal space, ultrahomogeneous spaces, functor, extensions of isometries

**AMS Subject Classification:** 54C20 54E40 54E50

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