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1995/1996 Some properties of (Φ)-uniformly symmetrically porous sets
Marek Balcerzak, Wojciech Wojdowski
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Real Anal. Exchange 21(1): 330-334 (1995/1996).


We prove that each perfect linear set contains a perfect set which is (\(\Phi\))-uniformly symmetrically porous (Theorem 1). In the hyperspace of all nonempty compact sets in \([0,1]\) (endowed with the Hausdorff distance), the (\(\Phi\))-uniformly symmetrically porous nonempty compact sets form a \(G_\delta\) residual subspace (Theorem 2). We infer that the\linebreak (\(\Phi\))-uniformly symmetrically porous perfect sets form a \(G_\delta\) residual set in the space of all perfect sets in \([0,1]\) (Theorem 3).


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Marek Balcerzak. Wojciech Wojdowski. "Some properties of (Φ)-uniformly symmetrically porous sets." Real Anal. Exchange 21 (1) 330 - 334, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0851.26002
MathSciNet: MR1377544

Primary: 04A15 , 26A21 , 54B20 , 54E52

Keywords: Hausdorff metric , perfect set , porous set , Residual set

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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