Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $s$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A78, 28A80, 54F45, 57N35

Retrieve articles in all journals with MSC: 28A78, 28A80, 54F45, 57N35


Additional Information

Keywords: Hausdorff dimension, Cantor set, fractal, wild, demension, similitude
Article copyright: © Copyright 1992 American Mathematical Society