# 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 Jennifer 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

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