Geodesic
Functor of extension of $\Lambda$-isometric maps between central subsets of the unbounded Urysohn universal space
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 541-549

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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.
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.
Classification : 54C20, 54E40, 54E50
Keywords: Urysohn's universal space; ultrahomogeneous spaces; functor; extensions of isometries 
Niemiec, Piotr. Functor of extension of $\Lambda$-isometric maps between central subsets of the unbounded Urysohn universal space. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 3, pp. 541-549. http://geodesic.mathdoc.fr/item/CMUC_2010_51_3_a14/
@article{CMUC_2010_51_3_a14,
     author = {Niemiec, Piotr},
     title = {Functor of extension of $\Lambda$-isometric maps between central subsets of the unbounded {Urysohn} universal space},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {541--549},
     year = {2010},
     volume = {51},
     number = {3},
     mrnumber = {2741886},
     zbl = {1224.54044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_3_a14/}
}
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