Hausdorff dimension of wild fractals

Rushing, T. B.

doi:10.1090/S0002-9947-1992-1162104-8

Hausdorff dimension of wild fractals
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Trans. Amer. Math. Soc. 334 (1992), 597-613 Request permission

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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