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1996/1997 The Hausdorff dimension of the hyperspace of compact sets
Mark McClure
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Real Anal. Exchange 22(2): 611-625 (1996/1997).


Let \((X,\rho)\) be a separable metric space and let \((\mathcal{K}(X),\widetilde{\rho})\) denote the space of non-empty compact subsets of \(X\) with the Hausdorff metric. The purpose of this paper is to investigate the relationship of the Hausdorff dimension of a set \(E \subset X\) to that of \(\mathcal{K}(E) \subset \mathcal{K}(X)\).


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Mark McClure. "The Hausdorff dimension of the hyperspace of compact sets." Real Anal. Exchange 22 (2) 611 - 625, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0943.28013
MathSciNet: MR1460975

Primary: 28A78 , 28C20 , 54B20

Keywords: fractal dimensions , Hausdorff measure , hyperspace

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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