I have a question about Hausdorff dimension. Suppose S is a compact subset of $\mathbb{R}^n$ whose Hausdorff dimension is zero. Does it follow that S can be covered by a finite DISJOINT union of closed disks with arbitrary small (positive) radius?
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$\begingroup$ Do you want the disks to be disjoint in $\mathbb R^n$ instead of forming a disjoint family when intersected with the set in question? I think the latter you can do simply by total disconnectedness. $\endgroup$– TeriCommented Feb 3, 2018 at 20:50
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$\begingroup$ @Teri I actually want the disks to be disjoint in $\mathbb{R}^n$. $\endgroup$– AndreaCommented Feb 3, 2018 at 21:24
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