Real Analysis Exchange

Some properties of (Φ)-uniformly symmetrically porous sets

Marek Balcerzak and Wojciech Wojdowski

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Abstract

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

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

Dates
First available in Project Euclid: 3 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1341343250

Mathematical Reviews number (MathSciNet)
MR1377544

Zentralblatt MATH identifier
0851.26002

Subjects
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

Keywords
porous set perfect set residual set Hausdorff metric

Citation

Balcerzak, Marek; Wojdowski, Wojciech. Some properties of (Φ)-uniformly symmetrically porous sets. Real Anal. Exchange 21 (1995), no. 1, 330--334. https://projecteuclid.org/euclid.rae/1341343250


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References

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