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arXiv · 2406.14509

Consistency and independence phenomena involving cellular-Lindelof spaces

Rodrigo Hernández-Gutiérrez·Santi Spadaro
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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 $\omega_1$ 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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Rodrigo Hernández-Gutiérrez, Santi Spadaro. 2024-06-20. Consistency and independence phenomena involving cellular-Lindelof spaces. https://arxiv.org/abs/2406.14509

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