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arXiv · 2211.01439

Inter model sets in $\mathbb R^d$ are model sets

Christoph Richard·Nicolae Strungaru
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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.

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Christoph Richard, Nicolae Strungaru. 2022-11-02. Inter model sets in $\mathbb R^d$ are model sets. https://doi.org/10.1016/j.indag.2023.06.007

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