Rudin-like sets and hereditary families of compact sets
Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 97-116
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Étienne Matheron 1 ; Miroslav Zelený 2
@article{10_4064_fm185_2_1,
author = {\'Etienne Matheron and Miroslav Zelen\'y},
title = {Rudin-like sets and hereditary families of compact sets},
journal = {Fundamenta Mathematicae},
pages = {97--116},
publisher = {mathdoc},
volume = {185},
number = {2},
year = {2005},
doi = {10.4064/fm185-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm185-2-1/}
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TY - JOUR AU - Étienne Matheron AU - Miroslav Zelený TI - Rudin-like sets and hereditary families of compact sets JO - Fundamenta Mathematicae PY - 2005 SP - 97 EP - 116 VL - 185 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm185-2-1/ DO - 10.4064/fm185-2-1 LA - en ID - 10_4064_fm185_2_1 ER -
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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