The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum

DOI10.1134/S0081543811080050zbMath1301.51015MaRDI QIDQ741166

Alexander Magazinov

Publication date: 10 September 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Delone setbi-Lipschitz class

Mathematics Subject Classification ID

General theory of distance geometry (51K05) Cardinal characteristics of the continuum (03E17) Euclidean geometries (general) and generalizations (51M05)

Related Items (8)

Discrepancy and rectifiability of almost linearly repetitive Delone sets ⋮ Continuously many bounded displacement non-equivalences in substitution tiling spaces ⋮ A dichotomy for bounded displacement equivalence of Delone sets ⋮ Divergence of separated nets with respect to displacement equivalence ⋮ Highly irregular separated nets ⋮ Bounded displacement non-equivalence in substitution tilings ⋮ Mapping \(n\) grid points onto a square forces an arbitrarily large Lipschitz constant ⋮ Separated nets in nilpotent groups

Cites Work

• Separated nets in Euclidean space and Jacobians of biLipschitz maps
• Lipschitz maps and nets in Euclidean space
• Homogeneous trees are bilipschitz equivalent
• Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture

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