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- W2595653878 abstract "Our aim is to find the minimal Hausdorff dimension of the union of scaled and/or rotated copies of the k-skeleton of a fixed polytope centered at the points of a given set. For many of these problems, we show that a typical arrangement in the sense of Baire category gives minimal Hausdorff dimension. In particular, this proves a conjecture of R. Thornton. Our results also show that Nikodym sets are typical among all sets which contain, for every x∈Rn, a punctured hyperplane H∖{x} through x. With similar methods we also construct a Borel subset of Rn of Lebesgue measure zero containing a hyperplane at every positive distance from every point." @default.
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- W2595653878 date "2018-04-01" @default.
- W2595653878 modified "2023-10-17" @default.
- W2595653878 title "Small unions of affine subspaces and skeletons via Baire category" @default.
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- W2595653878 doi "https://doi.org/10.1016/j.aim.2018.02.009" @default.
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