First countable spaces without point-countable π-bases

• Autorzy: István Juhász , Lajos Soukup , Zoltán Szentmiklóssy
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54D70: Base properties
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54A35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 196
• Numer: 2
• Strony: 139-149

Daty

wydano

2007

Twórcy

autor

István Juhász

• Alfréd Rényi Institute of Mathematics, V. Reáltanoda utca, 13-15, H-1053 Budapest, Hungary

autor

Lajos Soukup

• Alfréd Rényi Institute of Mathematics, V. Reáltanoda utca, 13-15, H-1053 Budapest, Hungary

autor

Zoltán Szentmiklóssy

• Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm196-2-4