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Uniform perfectness of self-affine sets. (English) Zbl 1027.28012

It is proved that any self-affine set \(E\) in the Euclidean space which is not a singleton is uniformly perfect, that is, there is a universal constant \(c>0\) such that for any \(x\in E\) and \(0<r<\text{diam}E\), the annulus centered at \(x\) of radii \(cr\) and \(r\) meets \(E\).

MSC:

28A80 Fractals
28A78 Hausdorff and packing measures
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