Gδ covers of compact spaces

Santi Domenico Spadaro, Santi Spadaro, Paul Szeptycki

Risultato della ricerca: Articlepeer review

6 Citazioni (Scopus)


We solve a long standing question due to Arhangel'skii by constructing a compact space which has a Gδ cover with no continuum-sized (Gδ)-dense subcollection. We also prove that in a countably compact weakly Lindelöf normal space of countable tightness, every Gδ cover has a -sized subcollection with a Gδ-dense union and that in a Lindelöf space with a base of multiplicity continuum, every Gδ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Vega's celebrated theorem on the cardinality of homogeneous compacta of countable tightness.
Lingua originaleEnglish
pagine (da-a)252-263
Numero di pagine12
RivistaActa Mathematica Hungarica
Stato di pubblicazionePublished - 2018

All Science Journal Classification (ASJC) codes

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