Geodesic
Rudin-like sets and hereditary families of compact sets
Étienne Matheron 1   ; Miroslav Zelený 2
1 Université Bordeaux 1 351 cours de la Libération 33405 Talence Cedex, France
2 Charles University Faculty of Mathematics and Physics Sokolovská 83 186 75, Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 97-116 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm185-2-1
Keywords: comeager hereditary family compact sets have dense delta subfamily which hereditary using prove abstract result which implies existence independent mathcal sets meagerness mathcal sets property baire generalizations classical results mycielski finally natural examples sigma delta sets

Étienne Matheron  1   ; Miroslav Zelený  2

1 Université Bordeaux 1 351 cours de la Libération 33405 Talence Cedex, France
2 Charles University Faculty of Mathematics and Physics Sokolovská 83 186 75, Praha 8, Czech Republic 
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Étienne Matheron; Miroslav Zelený. Rudin-like sets and hereditary families of compact sets. Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 97-116. doi: 10.4064/fm185-2-1

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