Description

• Title:
  Characterizing Lipschitz images of injective metric spaces
• Creator:
  Banakh, Taras;
  Bąk, Judyta;
  Garbulińska-Węgrzyn, Joanna;
  Nowak, Magdalena;
  Popławski, Michał
• Description:
  A metric space $X$ is {\em injective} if every non-expanding map $f \colon B\to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $\overline f \colon A\to X$. We prove that a metric space $X$ is a Lipschitz image of an injective metric space if and only if $X$ is {\em Lipschitz connected} in the sense that for every points $x,y\in X$, there exists a Lipschitz map $f \colon [0,1]\to X$ such that $f(0)=x$ and $f(1)=y$. In this case the metric space $X$ carries a well-defined intrinsic metric. A metric space $X$ is a Lipschitz image of a compact injective metric space if and only if $X$ is compact, Lipschitz connected and its intrinsic metric is totally bounded. A metric space $X$ is a Lipschitz image of a separable injective metric space if and only if $X$ is a Lipschitz image of the Urysohn universal metric space if and only if $X$ is analytic, Lipschitz connected and its intrinsic metric is separable.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 22;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62314/42829 ;https://apcz.umk.pl/TMNA/article/view/62314/42830
• Subject:
  Injective metric space;
  Lipschitz map;
  Lipschitz image;
  Urysohn metric space;
  Lipschitz connected metric space;
  Primary: 54E35, 54E40;
  Secondary: 51F30, 54C55, 54E45, 54E50, 54F15
• Identifier: https://apcz.umk.pl/TMNA/article/view/62314
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other