Rudin-like sets and hereditary families of compact sets

Volume 185 / 2005

Étienne Matheron, Miroslav Zelený Fundamenta Mathematicae 185 (2005), 97-116 MSC: 03E15, 28A05, 43A46. DOI: 10.4064/fm185-2-1


We show that a comeager ${\bf \Pi }_1^1$ hereditary family of compact sets must have a dense $G_\delta $ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ${{\mathcal M}}_0$-sets, the meagerness of ${\mathcal U}_0$-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_{\sigma \delta }$ sets.


  • Étienne MatheronUniversité Bordeaux 1
    351 cours de la Libération
    33405 Talence Cedex, France
  • Miroslav ZelenýCharles University
    Faculty of Mathematics and Physics
    Sokolovská 83
    186 75, Praha 8, Czech Republic

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