Metric transformations of the real line
type: Item
instance of: scholarly article
title: Metric transformations of the real line
zbMATH Open document ID: 0582.51009
DOI: 10.1216/RMJ-1985-15-1-199
author: Daryl Tingley
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: A metric transformation between two metric spaces is a function f such that \(d_ 2(f(x),f(y))=\rho (d_ 1(x,y))\) for some function \(\rho\) (\(\rho\) the so-called scale function of f). In this paper all metric transformations between \({\mathbb{R}}\) and \(E^ n\) are characterized. In a 1938 paper, von Neumann and Schönberg characterized all continuous metric transformations of \({\mathbb{R}}\) into Hilbert space. Thus the significant contribution of this paper is in characterizing the discontinuous transformations, of which there are many, from \({\mathbb{R}}\) into \(E^ n\).
Mathematics Subject Classification ID: 51K05
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 51F99
zbMATH DE Number: 3931894
zbMATH Keywords: screw curve
zbMATH Keywords: multidimensional scaling
zbMATH Keywords: metric transformation
zbMATH Keywords: scale function
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-1-199
OpenAlex ID: W1997221818
description: scientific article; zbMATH DE number 3931894