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.File in questo prodotto:
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