Abstract
A space X is said to be cellular-Lindelöf if, for every family \(\mathcal U\) of disjoint non-empty open sets of X, there is a Lindelöf subspace \(L\subset X\), such that \(U\cap L \not = \emptyset \) for every \(U\in \mathcal U\). This class of spaces was introduced by Bella and Spadaro in 2007. In this paper, our main result is to show that the Pixley–Roy space \(\mathcal F[X]\) is cellular-Lindelöf if and only if it is CCC. We also establish a cardinal inequality for cellular-Lindelöf spaces which have a symmetric g-function. Some open questions are posed.
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Acknowledgements
The authors also would like to express his sincere appreciation to the referee for his/her careful reading the paper and many helpful comments which greatly improved the paper. In particular, the final part of the proof of Theorem 3.5 is due to the referee’s suggestion.
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Communicated by Mohammad Reza Koushesh.
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W.-F. Xuan is supported by NSFC project 11801271. Y.-K. Song is supported by NSFC project 11771029.
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Xuan, WF., Song, YK. Further Results on Cellular-Lindelöf Spaces. Bull. Iran. Math. Soc. 46, 669–674 (2020). https://doi.org/10.1007/s41980-019-00283-7
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DOI: https://doi.org/10.1007/s41980-019-00283-7