## Real Analysis Exchange

### Some properties of (Φ)-uniformly symmetrically porous sets

#### 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

https://projecteuclid.org/euclid.rae/1341343250

Mathematical Reviews number (MathSciNet)
MR1377544

Zentralblatt MATH identifier
0851.26002

#### 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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