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A relationship between packing and topological dimensions

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

H. Joyce
H. Joyce
Affiliation:
University of Jyväskylä, Department of Mathematics, P.O. Box 35, FIN-40351, Jyväskylä, Finland.
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Abstract

The relationship between the topological dimension of a separable metric space and the Hausdorff dimensions of its homeomorphic images has been known for some time. In this note we consider topological and packing dimensions, and show that if X is a separable metric space, then

where and denote the topological and packing dimensions of X, respectively.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 43 - 53
Copyright
Copyright © University College London 1998

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