# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Inscribing compact non-$\sigma$-porous sets into analytic non-$\sigma$-porous sets

### Tom 185 / 2005

Fundamenta Mathematicae 185 (2005), 19-39 MSC: 54H05, 28A05. DOI: 10.4064/fm185-1-2

#### Streszczenie

The main aim of this paper is to give a simpler proof of the following assertion. Let $A$ be an analytic non-$\sigma$-porous subset of a locally compact metric space ,$E$. Then there exists a compact non-$\sigma$-porous subset of $A$. Moreover, we prove the above assertion also for $\sigma$-$\bf P$-porous sets, where ${\bf P}$ is a porosity-like relation on $E$ satisfying some additional conditions. Our result covers $\sigma$-$\langle g \rangle$-porous sets, $\sigma$-porous sets, and $\sigma$-symmetrically porous sets.

#### Autorzy

• Miroslav ZelenýCharles University
Faculty of Mathematics and Physics, KMA
Sokolovská 83
Praha 8, 186 00, Czech Republic
e-mail
• Luděk ZajíčekFaculty of Mathematics and Physics, KMA
Charles University
Sokolovská 83
Praha 8, 186 00, Czech Republic
e-mail

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