First countable spaces without point-countable π-bases

István Juhász, Lajos Soukup, and Zoltán Szentmiklóssy. "First countable spaces without point-countable π-bases." Fundamenta Mathematicae 196.2 (2007): 139-149. <http://eudml.org/doc/283230>.

@article{IstvánJuhász2007,
abstract = { We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a first countable, hereditarily Lindelöf regular space having uncountable π-weight and ω₁ as a caliber (of course, such a space cannot have a point-countable π-base). },
author = {István Juhász, Lajos Soukup, Zoltán Szentmiklóssy},
journal = {Fundamenta Mathematicae},
keywords = {first countable space, point-countable -base, Lindelöf space, CCC space, caliber},
language = {eng},
number = {2},
pages = {139-149},
title = {First countable spaces without point-countable π-bases},
url = {http://eudml.org/doc/283230},
volume = {196},
year = {2007},
}

TY - JOUR
AU - István Juhász
AU - Lajos Soukup
AU - Zoltán Szentmiklóssy
TI - First countable spaces without point-countable π-bases
JO - Fundamenta Mathematicae
PY - 2007
VL - 196
IS - 2
SP - 139
EP - 149
AB - We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that ∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large); ∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ; ∙ it is consistent to have a first countable, hereditarily Lindelöf regular space having uncountable π-weight and ω₁ as a caliber (of course, such a space cannot have a point-countable π-base).
LA - eng
KW - first countable space, point-countable -base, Lindelöf space, CCC space, caliber
UR - http://eudml.org/doc/283230
ER -