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.

S. Spadaro, & P. Szeptycki (2018). Gδ covers of compact spaces. ACTA MATHEMATICA HUNGARICA, 154(1), 252-263 [10.1007/s10474-017-0785-4].

Gδ covers of compact spaces

S. Spadaro
;
2018

Abstract

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.
Settore MAT/03 - Geometria
https://link.springer.com/article/10.1007/s10474-017-0785-4
S. Spadaro, & P. Szeptycki (2018). Gδ covers of compact spaces. ACTA MATHEMATICA HUNGARICA, 154(1), 252-263 [10.1007/s10474-017-0785-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/480994
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