2016/05/18 by Spadaro, Santi, Szeptycki, Paul
#FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1605.05630
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 \mathfrakc-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.