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EnglishA space is said to be "almost discretely Lindelöf" if every discrete subset can be covered by a Lindelöf subspace. Juhász, Tkachuk and Wilson asked whether every almost discretely Lindelöf first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under 2<= (which is a consequence of Martin's Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhász, Soukup and Szentmiklóssy. We conclude with a few related results and questions.
| Titolo: | On the cardinality of almost discretely Lindelof spaces |
| Autori interni: | SPADARO, SANTI DOMENICO (Corresponding) |
| Data di pubblicazione: | 2018 |
| Rivista: | |
| Abstract: | A space is said to be "almost discretely Lindelöf" if every discrete subset can be covered by a Lindelöf subspace. Juhász, Tkachuk and Wilson asked whether every almost discretely Lindelöf first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under 2<= (which is a consequence of Martin's Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhász, Soukup and Szentmiklóssy. We conclude with a few related results and questions. |
| Handle: | http://hdl.handle.net/20.500.11769/365611 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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