6533b7d0fe1ef96bd125a088
RESEARCH PRODUCT
Gδ covers of compact spaces
S. SpadaroP. Szeptyckisubject
Cardinal function Gδ-cover Lindelof degree Homogeneous spaceSettore MAT/03 - Geometriadescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |