Inter model sets in $\mathbb R^d$ are model sets
Mathematical Physics
2024-09-05 v1 math.MP
Abstract
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original window. Our results hold in fact for a class beyond inter model sets, which we call almost model sets.
Keywords
Cite
@article{arxiv.2211.01439,
title = {Inter model sets in $\mathbb R^d$ are model sets},
author = {Christoph Richard and Nicolae Strungaru},
journal= {arXiv preprint arXiv:2211.01439},
year = {2024}
}