We give a metric characterization of snowflakes of Euclidean spaces. Namely, we prove that a metric space is isometric to ℝn equipped with a distance (dE)ϵ, for some n ∈ ℕ0 and ∈ ∈ (0, 1), where dE is the Euclidean distance, if and only if it is locally compact, and 2-point isometrically homogeneous, and admits dilations of any factor.

A metric characterization of snowflakes of Euclidean spaces

Le Donne, Enrico
2016-01-01

Abstract

We give a metric characterization of snowflakes of Euclidean spaces. Namely, we prove that a metric space is isometric to ℝn equipped with a distance (dE)ϵ, for some n ∈ ℕ0 and ∈ ∈ (0, 1), where dE is the Euclidean distance, if and only if it is locally compact, and 2-point isometrically homogeneous, and admits dilations of any factor.
2016
Kinneberg, Kyle; Le Donne, Enrico
File in questo prodotto:
File Dimensione Formato  
KinnebergLeDonne-SFsofRn-2016-03-27.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 304.61 kB
Formato Adobe PDF
304.61 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/978753
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact