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Corpus ID: 189898160

Large Sets with Small Injective Projections

@article{Coen2019LargeSW,
title={Large Sets with Small Injective Projections},
author={Frank Coen and N. Gillman and T. Keleti and Dylan A. King and J. Zhu},
journal={arXiv: Metric Geometry},
year={2019}
}

Let $\ell_1,\ell_2,\dots$ be a countable collection of lines in ${\mathbb R}^d$. For any $t \in [0,1]$ we construct a compact set $\Gamma\subset{\mathbb R}^d$ with Hausdorff dimension $d-1+t$ which projects injectively into each $\ell_i$, such that the image of each projection has dimension $t$. This immediately implies the existence of homeomorphisms between certain Cantor-type sets whose graphs have large dimensions. As an application, we construct a collection $E$ of disjoint, non-parallel… Expand