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arXiv · 2204.08428

Thickness and a gap lemma in $\mathbb{R}^d$

Alexia Yavicoli
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Abstract

We give a definition of thickness in $\mathbb{R}^d$ that is useful even for totally disconnected sets, and prove a Gap Lemma type result. We also guarantee an interval of distances in any direction in thick compact sets, relate thick sets (for this definition of thickness) with winning sets, give a lower bound for the Hausdorff dimension of the intersection of countably many of them, a result guaranteeing the presence of large patterns, and lower bounds for the Hausdorff dimension of a set in relationship with its thickness.

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Alexia Yavicoli. 2022-04-15. Thickness and a gap lemma in $\mathbb{R}^d$. https://arxiv.org/abs/2204.08428

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