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EnglishA space X is said to be "cellular-Lindelöf" if for every cellular family there is a Lindelöf subspace L of X which meets every element of . Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular Gδ-diagonal has cardinality at most 2. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2<= and that every normal cellular Lindelöf space with a Gδ-diagonal of rank 2 has cardinality at most continuum.
| Titolo: | Cardinal invariants of cellular Lindelof spaces |
| Autori interni: | SPADARO, SANTI DOMENICO (Corresponding) |
| Data di pubblicazione: | 2019 |
| Rivista: | |
| Abstract: | A space X is said to be "cellular-Lindelöf" if for every cellular family there is a Lindelöf subspace L of X which meets every element of . Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular Gδ-diagonal has cardinality at most 2. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2<= and that every normal cellular Lindelöf space with a Gδ-diagonal of rank 2 has cardinality at most continuum. |
| Handle: | http://hdl.handle.net/20.500.11769/365617 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| CellularLindelofFinale.pdf | Versione Editoriale (PDF) | Administrator |
http://hdl.handle.net/20.500.11769/365617
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