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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Hausdorff dimension of wild fractals
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by T. B. Rushing PDF
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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • 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