IJPAM: Volume 14, No. 2 (2004)

FRACTAL DIMENSIONS OF INFINITE
PRODUCT SPACES

Kathryn E. Hare$^1$, Jan-Olav Rönning$^2$
$^1$Department of Pure Mathematics
University of Waterloo
200 University Avenue West
Waterloo, Ont., N2L 3G1, CANADA
e-mail: kehare@uwaterloo.ca
$^2$Institutionen för Naturvetenskap
Högskolan i Skövde
Box 408, S-541 28, Skövde, SWEDEN
e-mail: jan-olav.ronning@inv.his.se


Abstract.In this paper the fractal geometry of compact subsets of the infinite dimensional metric space $\mathbb{R}^{\infty}$ is studied. Our main interest is in products of self-similar or Cantor-like sets, and we show that there are many differences between infinite products of these sets in $\mathbb{R}^{\infty}$ and finite products in Euclidean space.

Received: February 4, 2004

AMS Subject Classification: 28A80

Key Words and Phrases: Hausdorff dimension, box dimension, infinite product, self-similar set, Cantor set

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 2