Consistency and independence phenomena involving cellular-Lindelof spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910495844335616 |
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| author | Hernández-Gutiérrez, Rodrigo Spadaro, Santi |
| author_facet | Hernández-Gutiérrez, Rodrigo Spadaro, Santi |
| contents | The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro in 2018. We solve two questions of Alas, Gutierrez-Dominguez and Wilson by constructing consistent examples of a normal almost cellular-Lindelöf space which is neither cellular-Lindelöf nor weakly Lindelöf and a Tychonoff cellular-Lindelöf space of Lindelöf degree $ω_1$ and uncountable weak Lindelöf degree for closed sets. We also construct a ZFC example of a space for which both the cellular-Lindelöf property and normality are undetermined in ZFC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_14509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistency and independence phenomena involving cellular-Lindelof spaces Hernández-Gutiérrez, Rodrigo Spadaro, Santi General Topology Logic Primary: 54A25, 54D20, 03E17, Secondary: 54D15, 54G10, 03E35 The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro in 2018. We solve two questions of Alas, Gutierrez-Dominguez and Wilson by constructing consistent examples of a normal almost cellular-Lindelöf space which is neither cellular-Lindelöf nor weakly Lindelöf and a Tychonoff cellular-Lindelöf space of Lindelöf degree $ω_1$ and uncountable weak Lindelöf degree for closed sets. We also construct a ZFC example of a space for which both the cellular-Lindelöf property and normality are undetermined in ZFC. |
| title | Consistency and independence phenomena involving cellular-Lindelof spaces |
| topic | General Topology Logic Primary: 54A25, 54D20, 03E17, Secondary: 54D15, 54G10, 03E35 |
| url | https://arxiv.org/abs/2406.14509 |