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arxiv: 1812.09542 · v1 · pith:DTDK67AX · submitted 2018-12-22 · math.MG

Coincidence and noncoincidence of dimensions in compact subsets of [0,1]

Andrew Mitchell , Lars Olsen This is my paper

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classification math.MG
keywords dimensionequalcompacthausdorfflowerpackingassouadcoincidence
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We show that given any six numbers $r,s,t,u,v,w \in (0,1]$ satisfying $r \leq s \leq \min(t,u) \leq \max(t,u) \leq v \leq w$, it is possible to construct a compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified box dimension equal to $s$, packing dimension equal to $t$, lower box dimension equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to $w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing set.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On strong algebrability and spaceability of continuous functions and fractal dimensions

    math.FA 2026-06 unverdicted novelty 5.0

    Intersections of continuous functions with prescribed Hausdorff dimension s and box dimensions r,t are shown to be strongly c-algebrable and spaceable, plus related lineability results.