Consistency and independence phenomena involving cellular-Lindelof spaces
General Topology
2024-06-21 v1 Logic
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 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.
Keywords
Cite
@article{arxiv.2406.14509,
title = {Consistency and independence phenomena involving cellular-Lindelof spaces},
author = {Rodrigo Hernández-Gutiérrez and Santi Spadaro},
journal= {arXiv preprint arXiv:2406.14509},
year = {2024}
}