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

Tom 185 / 2005

Miroslav Zelený, Luděk Zajíček 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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