Strongly discrete subsets with Lindelöf closures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913292769820672 |
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| author | Bella, Angelo Spadaro, Santi |
| author_facet | Bella, Angelo Spadaro, Santi |
| contents | We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindelöf. After distinguishing this property from the Lindelöf property we make various remarks about cardinal invariants of SDL spaces. For example we prove that $|X| \leq 2^{χ(X)}$ for every SDL Urysohn space and that every SDL $P$-space of character $\leq ω_1$ is regular and has cardinality $\leq 2^{ω_1}$. Finally, we exploit our results to obtain some partial answers to questions about the cardinality of cellular-Lindelöf spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly discrete subsets with Lindelöf closures Bella, Angelo Spadaro, Santi General Topology We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindelöf. After distinguishing this property from the Lindelöf property we make various remarks about cardinal invariants of SDL spaces. For example we prove that $|X| \leq 2^{χ(X)}$ for every SDL Urysohn space and that every SDL $P$-space of character $\leq ω_1$ is regular and has cardinality $\leq 2^{ω_1}$. Finally, we exploit our results to obtain some partial answers to questions about the cardinality of cellular-Lindelöf spaces. |
| title | Strongly discrete subsets with Lindelöf closures |
| topic | General Topology |
| url | https://arxiv.org/abs/2404.00455 |