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

Open Mathematics (2013)

- Volume: 11, Issue: 9, page 1635-1642
- ISSN: 2391-5455

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topSüleyman Önal, and Çetin Vural. "On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces." Open Mathematics 11.9 (2013): 1635-1642. <http://eudml.org/doc/269192>.

@article{SüleymanÖnal2013,

abstract = {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.},

author = {Süleyman Önal, Çetin Vural},

journal = {Open Mathematics},

keywords = {Metacompact; MetaLindelöf; Product spaces; Noetherian; Rank; metacompact; metaLindelöf; product spaces; rank},

language = {eng},

number = {9},

pages = {1635-1642},

title = {On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces},

url = {http://eudml.org/doc/269192},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Süleyman Önal

AU - Çetin Vural

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

JO - Open Mathematics

PY - 2013

VL - 11

IS - 9

SP - 1635

EP - 1642

AB - 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.

LA - eng

KW - Metacompact; MetaLindelöf; Product spaces; Noetherian; Rank; metacompact; metaLindelöf; product spaces; rank

UR - http://eudml.org/doc/269192

ER -

## References

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