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Hausdorff dimension of wild fractals


Author: T. B. Rushing
Journal: Trans. Amer. Math. Soc. 334 (1992), 597-613
MSC: Primary 28A78; Secondary 28A80, 54F45, 57N35
DOI: https://doi.org/10.1090/S0002-9947-1992-1162104-8
MathSciNet review: 1162104
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Abstract: We show that for every $ s \in [n - 2,n]$ there exists a homogeneously embedded wild Cantor set $ {C^s}$ in $ \mathbb{R}^n, n \geq 3$, of (local) Hausdorff dimension $ s$. Also, it is shown that for every $ s \in [n - 2,n]$ and for any integer $ k \ne n$ such that $ 1 \leq k \leq s$, there exist everywhere wild $ k$-spheres and $ k$-cells, in $ \mathbb{R}^n, n \geq 3$, of (local) Hausdorff dimension $ s$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1162104-8
Keywords: Hausdorff dimension, Cantor set, fractal, wild, demension, similitude
Article copyright: © Copyright 1992 American Mathematical Society

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