Xie, Feng; Yin, Yongcheng; Sun, Yeshun Uniform perfectness of self-affine sets. (English) Zbl 1027.28012 Proc. Am. Math. Soc. 131, No. 10, 3053-3057 (2003). 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 \(E\). Reviewer: José-Manuel Rey (Madrid) Cited in 9 Documents MSC: 28A80 Fractals 28A78 Hausdorff and packing measures Keywords:self-affine sets; uniformly perfect sets PDFBibTeX XMLCite \textit{F. Xie} et al., Proc. Am. Math. Soc. 131, No. 10, 3053--3057 (2003; Zbl 1027.28012) Full Text: DOI