Functor of extension of Λ -isometric maps between central subsets of the unbounded Urysohn universal space

Piotr Niemiec

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 3, page 541-549
  • ISSN: 0010-2628

Abstract

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The aim of the paper is to prove that in the unbounded Urysohn universal space 𝕌 there is a functor of extension of Λ -isometric maps (i.e. dilations) between central subsets of 𝕌 to Λ -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group ℝ ∖ { 0 } acts continuously on 𝕌 by Λ -isometries.

How to cite

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Niemiec, Piotr. "Functor of extension of $\Lambda $-isometric maps between central subsets of the unbounded Urysohn universal space." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 541-549. <http://eudml.org/doc/38149>.

@article{Niemiec2010,
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 \lbrace 0\rbrace $ acts continuously on $\mathbb \{U\}$ by $\Lambda $-isometries.},
author = {Niemiec, Piotr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Urysohn's universal space; ultrahomogeneous spaces; functor; extensions of isometries; Urysohn's universal space; ultrahomogeneous space; functor; extension of isometries},
language = {eng},
number = {3},
pages = {541-549},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Functor of extension of $\Lambda $-isometric maps between central subsets of the unbounded Urysohn universal space},
url = {http://eudml.org/doc/38149},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Niemiec, Piotr
TI - Functor of extension of $\Lambda $-isometric maps between central subsets of the unbounded Urysohn universal space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 541
EP - 549
AB - 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 \lbrace 0\rbrace $ acts continuously on $\mathbb {U}$ by $\Lambda $-isometries.
LA - eng
KW - Urysohn's universal space; ultrahomogeneous spaces; functor; extensions of isometries; Urysohn's universal space; ultrahomogeneous space; functor; extension of isometries
UR - http://eudml.org/doc/38149
ER -

References

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