On the cardinality of almost discretely Lindelof spaces
- Autori: A. Bella; S. Spadaro
- Anno di pubblicazione: 2018
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/480967
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.