Consistency and independence phenomena involving cellular-Lindelof spaces
Abstract
The cellular-Lindel\"of property is a common generalization of the Lindel\"of 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-Lindel\"of space which is neither cellular-Lindel\"of nor weakly Lindel\"of and a Tychonoff cellular-Lindel\"of space of Lindel\"of degree ω1 and uncountable weak Lindel\"of degree for closed sets. We also construct a ZFC example of a space for which both the cellular-Lindel\"of property and normality are undetermined in ZFC.
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