On the cardinality of almost discretely Lindelof spaces

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MONATSHEFTE FUR MATHEMATIK; v. 186, n. 2, p. 345-353, JUN 2018.
• Citações Web of Science: 7

Resumo

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)

• Processo FAPESP: 13/14640-1 - Conjuntos discretos e invariantes cardinais em topologia conjuntista
• Beneficiário: Santi Domenico Spadaro
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado