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.

A. Bella, & S. Spadaro (2018). On the cardinality of almost discretely Lindelof spaces. MONATSHEFTE FÜR MATHEMATIK, 186(2), 345-353 [10.1007/s00605-017-1112-4].

On the cardinality of almost discretely Lindelof spaces

S. Spadaro
2018

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.
Settore MAT/03 - Geometria
A. Bella, & S. Spadaro (2018). On the cardinality of almost discretely Lindelof spaces. MONATSHEFTE FÜR MATHEMATIK, 186(2), 345-353 [10.1007/s00605-017-1112-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480967
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