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.
On the cardinality of almost discretely Lindelof spaces
A. Bella;S. Spadaro
2018-01-01
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
ADLFinale.pdf
solo gestori archivio
Tipologia:
Versione Editoriale (PDF)
Dimensione
583.78 kB
Formato
Adobe PDF
|
583.78 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.