Real Analysis Exchange

Some properties of (Φ)-uniformly symmetrically porous sets

Marek Balcerzak and Wojciech Wojdowski

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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).

Article information

Real Anal. Exchange, Volume 21, Number 1 (1995), 330-334.

First available in Project Euclid: 3 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 54E52: Baire category, Baire spaces 54B20: Hyperspaces 04A15

porous set perfect set residual set Hausdorff metric


Balcerzak, Marek; Wojdowski, Wojciech. Some properties of (Φ)-uniformly symmetrically porous sets. Real Anal. Exchange 21 (1995), no. 1, 330--334.

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