Consistency and independence phenomena involving cellular-Lindelof spaces

2024/06/20 by Hernández-Gutiérrez, Rodrigo, Spadaro, Santi
#03E17 #03E35 #54D20 #54G10 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Primary: 54A25 #Secondary: 54D15

paper · doi:10.48550/arxiv.2406.14509

Abstract

The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro in 2018. We solve two questions of Alas, Gutierrez-Dominguez and Wilson by constructing consistent examples of a normal almost cellular-Lindelöf space which is neither cellular-Lindelöf nor weakly Lindelöf and a Tychonoff cellular-Lindelöf space of Lindelöf degree ω₁ and uncountable weak Lindelöf degree for closed sets. We also construct a ZFC example of a space for which both the cellular-Lindelöf property and normality are undetermined in ZFC.

Related

• Cardinal invariants of cellular-Lindelof spaces
• Productivity of cellular-Lindelof spaces
• On Cellular-Compact and related spaces
• Weakly linearly Lindel"of monotonically normal spaces are Lindel"of
• First countable and almost discretely Lindelöf T₃ spaces have cardinality at most continuum