2018/12/22 by Mitchell, Andrew, Olsen, Lars · 1 citation
#28A78 (Primary) #28A80 (Secondary) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1812.09542
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.