Strongly discrete subsets with Lindel\'of closures
| Autor: | Bella, Angelo, Spadaro, Santi |
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| Rok vydání: | 2024 |
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| Zdroj: | Topology Proceedings 59 (2022), 89--98 |
| Druh dokumentu: | Working Paper |
| Popis: | We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindel\"of. After distinguishing this property from the Lindel\"of property we make various remarks about cardinal invariants of SDL spaces. For example we prove that $|X| \leq 2^{\chi(X)}$ for every SDL Urysohn space and that every SDL $P$-space of character $\leq \omega_1$ is regular and has cardinality $\leq 2^{\omega_1}$. Finally, we exploit our results to obtain some partial answers to questions about the cardinality of cellular-Lindel\"of spaces. Comment: Dedicated to the memory of Phil Zenor |
| Databáze: | arXiv |
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