Regular spaces of small extent are ω-resolvable

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

Abstrakty

EN

We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable.
We also prove that any regular Lindelöf space X with |X| = Δ(X) = ω₁ is even ω₁-resolvable. The question whether regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open.

Kategorie tematyczne

• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54A35: Consistency and independence results
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 1
• Strony: 27-46

Daty

wydano

2015

Twórcy

autor

István Juhász

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u., 1053 Budapest, Hungary

autor

Lajos Soukup

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u., 1053 Budapest, Hungary

autor

Zoltán Szentmiklóssy

• Institute of Mathematics, Faculty of Science, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm228-1-3