Isometric embedding of finite ultrametric spaces in Banach spaces
type: Item
instance of: scholarly article
title: Isometric embedding of finite ultrametric spaces in Banach spaces
zbMATH Open document ID: 1071.54015
published in: Topology and its Applications
publication date: 2004-11-23T00:00:00Z
review text: Recall that a metric space \((X, d)\) is called ultrametric (or isosceles, or non-Archimedian) if \(d(x, z)\leq\max\{d(x, y),d(y, z)\}\) for all \(x,y,z\in X\). It was shown by \textit{B. Fichet} in [Classification and related methods of data analysis, Proc. 1st Conf. IFCS, Aachen/FRG 1987, 439--444 (1984; Zbl 0734.62002)] that every finite ultrametric space can be isometrically embedded into the Banach space \(l_p\) for each \(p\in[1,\infty]\). In this interesting paper it is shown that, in fact, every finite ultrametric space can be isometrically embedded into every infinite-dimensional Banach space.
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 2117940
zbMATH Keywords: ultrametric space
zbMATH Keywords: isosceles metric spaces
zbMATH Keywords: non-Archimedian metric space
zbMATH Keywords: isometric embedding
zbMATH Keywords: Banach space
author: S. Shkarin
reviewed by: Harald Brandenburg
MaRDI profile type: Publication
full work available at URL: j.topol.2003.12.002
OpenAlex ID: W1988842027
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DOI: 10.1016/J.TOPOL.2003.12.002
description: scientific article; zbMATH DE number 2117940