On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

• Autorzy: Süleyman Önal , Çetin Vural
• Języki publikacji: EN

Abstrakty

EN

We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.

Słowa kluczowe

EN

Metacompact; MetaLindelöf; Product spaces; Noetherian; Rank

Kategorie tematyczne

• 03E02: Partition relations
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1635-1642

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Süleyman Önal

• Middle East Technical University

autor

Çetin Vural

• Gazi Universitesi

Bibliografia

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• [9] Vural Ç., Some weaker forms of the chain (F) condition for metacompactness, J. Aust. Math. Soc., 2008, 84(2), 283–288 http://dx.doi.org/10.1017/S1446788708000037

Identyfikatory

DOI

10.2478/s11533-013-0271-3