Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
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

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1162104-8
PII: S 0002-9947(1992)1162104-8
Keywords: Hausdorff dimension, Cantor set, fractal, wild, demension, similitude
Article copyright: © Copyright 1992 American Mathematical Society