2018/12/22 by Andrew Mitchell, A. R. Mitchell, Lars Olsen +3 · 1 citation
Mathematics · #28A78 (Primary) #28A80 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #advanced mathematical theories #math.MG #msc:28A78 #msc:28A80
paper · pdf · doi:10.48550/arxiv.1812.09542
18 pages
arxiv created 2018/12/22 · openalex publication_date 2018/12/22 · arxiv updated 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that given any six numbers r,s,t,u,v,w ∈ (0,1] satisfying r ≤ s ≤ min(t,u) ≤ max(t,u) ≤ v ≤ 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.