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

Commentationes mathematicae Universitatis Carolinae

Piotr Niemiec¹ 

关键词: Urysohn's universal space;    ultrahomogeneous spaces;    functor;    extensions of isometries;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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.

【 授权许可】

CC BY