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On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces
Date
2013-09-01
Author
Önal, Süleyman
VURAL, ÇETİN
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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 a X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of omega-rank, then X is metaLindelof as well as a countable product of them. We also prove that if W satisfies omega-rank (F) and, for every x a X, W(x) is of the form W (0)(x) a(a) W (1)(x), where W (0)(x) is Noetherian and W (1)(x) consists of neighbourhoods of x, then X is metacompact.
Subject Keywords
Metacompact
,
Rank
,
Noetherian
,
Product spaces
,
MetaLindelof
URI
https://hdl.handle.net/11511/37378
Journal
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.2478/s11533-013-0271-3
Collections
Department of Mathematics, Article