Rudin-like sets and hereditary families of compact sets

Étienne Matheron, and Miroslav Zelený. "Rudin-like sets and hereditary families of compact sets." Fundamenta Mathematicae 185.2 (2005): 97-116. <http://eudml.org/doc/282702>.

@article{ÉtienneMatheron2005,
abstract = {We show that a comeager Π₁¹ hereditary family of compact sets must have a dense $G_δ$ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_\{σδ\}$ sets.},
author = {Étienne Matheron, Miroslav Zelený},
journal = {Fundamenta Mathematicae},
keywords = {comeager; meager; Baire property; hereditary family of compact sets},
language = {eng},
number = {2},
pages = {97-116},
title = {Rudin-like sets and hereditary families of compact sets},
url = {http://eudml.org/doc/282702},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Étienne Matheron
AU - Miroslav Zelený
TI - Rudin-like sets and hereditary families of compact sets
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 2
SP - 97
EP - 116
AB - We show that a comeager Π₁¹ hereditary family of compact sets must have a dense $G_δ$ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_{σδ}$ sets.
LA - eng
KW - comeager; meager; Baire property; hereditary family of compact sets
UR - http://eudml.org/doc/282702
ER -