Homogeneity properties of some \(\ell_1\)-spaces
type: Item
instance of: scholarly article
title: Homogeneity properties of some \(\ell_1\)-spaces
zbMATH Open document ID: 1088.54012
author: N. E. Zubov
published in: Discrete \& Computational Geometry
publication date: 2006-03-21T00:00:00Z
review text: Let \(\mathcal M\) be a family of subspaces of a metric space \(X\). The space \(X\) is \(\mathcal M\)-homogeneous if any isometry of two subspaces in \(\mathcal M\) can be extended to an isometry of \(X\). The author calls \(X\) fully homogeneous when \(\mathcal M\) is the family of all subspaces of \(X\). It is shown that a fully homogeneous subspace \(L\) of \(\mathbb R\) is either a two-point subspace or a subspace isometric to a subgroup of the additive group \(\mathbb R\), and that the space \(L^n\), where \(L\) is a fully homogeneous subspace of \(\mathbb R\), is \(\mathcal R\)-homogeneous, where \(\mathcal R\) is the family of subspaces that are products of subsets of \(L\).
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 5013772
zbMATH Keywords: homogeneous
zbMATH Keywords: fully homogeneous
zbMATH Keywords: isometry
zbMATH Keywords: metric space
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: s00454-005-1217-8
OpenAlex ID: W2048891420
DOI: 10.1007/S00454-005-1217-8
description: scientific article; zbMATH DE number 5013772