Functor of extension of contractions on Urysohn universal spaces

摘要

The aim of the paper is to show that there exists a functor of extension of contractions (i.e. nonexpansive maps) between compact subsets of a bounded Urysohn space (see Definition 2.1) to contractions acting on the whole space. The analogous result for the category of isometries between compact subsets of the unbounded Urysohn space is proved. Special properties of the functors are established.