On the cardinality of almost discretely Lindelof spaces

Author(s)

Bella, Angelo ^[1] ; Spadaro, Santi ^{[2, 1]}

Affiliation

^[1] Univ Catania, Dept Math & Comp Sci, Viale A Doria 6, I-95125 Catania - Italy

^[2] Univ Sao Paulo, IME, Rua Matao, 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: MONATSHEFTE FUR MATHEMATIK; v. 186, n. 2, p. 345-353, JUN 2018.
• Web of Science Citations: 7

Abstract

A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv: 1610.04506) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under 2< c = c (which is a consequence of Martin's Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof T3 spaces have cardinality at most continuum, preprint, arXiv: 1612.06651). We conclude with a few related results and questions. (AU)

• FAPESP's process: 13/14640-1 - Discrete sets and cardinal invariants in set-theoretic topology
• Grantee: Santi Domenico Spadaro
• Support Opportunities: Scholarships in Brazil - Post-Doctoral