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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0271-3,
author = {S\"uleyman \"Onal and \c Cetin Vural},
title = {On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1635-1642},
zbl = {06236723},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0271-3}
}
Süleyman Önal; Çetin Vural. On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces. Open Mathematics, Tome 11 (2013) pp. 1635-1642. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0271-3/
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