CONSISTENCY AND INDEPENDENCE PHENOMENA INVOLVING CELLULAR-LINDELÖF SPACES

Rodrigo Hernández-Gutiérrez; Santi Spadaro

doi:10.1090/proc/17224

CONSISTENCY AND INDEPENDENCE PHENOMENA INVOLVING CELLULAR-LINDELÖF SPACES

Rodrigo Hernández-Gutiérrez
, Santi Spadaro

Research output: Contribution to journal › Article › peer-review

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 [Monatsh. Math. 186 (2018), pp. 345–353]. We solve two questions of Alas, Gutiérrez-Domínguez and Wilson [Acta Math. Hungar. 167 (2022), pp 548–560] 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 almost cellular-Lindelöf property and normality are undetermined in ZFC.

Original language	English
Pages (from-to)	2701-2711
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	6
DOIs	https://doi.org/10.1090/proc/17224
State	Published - 1 Jun 2025
Externally published	Yes

Keywords

Cellular-Lindelöf
concentrated set
scale
tower
weak Lindelöf number

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/17224

Cite this

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title = "CONSISTENCY AND INDEPENDENCE PHENOMENA INVOLVING CELLULAR-LINDEL{\"O}F SPACES",

abstract = "The cellular-Lindel{\"o}f property is a common generalization of the Lindel{\"o}f property and the countable chain condition that was introduced by Bella and Spadaro [Monatsh. Math. 186 (2018), pp. 345–353]. We solve two questions of Alas, Guti{\'e}rrez-Dom{\'i}nguez and Wilson [Acta Math. Hungar. 167 (2022), pp 548–560] by constructing consistent examples of a normal almost cellular-Lindel{\"o}f space which is neither cellular-Lindel{\"o}f nor weakly Lindel{\"o}f and a Tychonoff cellular-Lindel{\"o}f space of Lindel{\"o}f degree ω1 and uncountable weak Lindel{\"o}f degree for closed sets. We also construct a ZFC example of a space for which both the almost cellular-Lindel{\"o}f property and normality are undetermined in ZFC.",

keywords = "Cellular-Lindel{\"o}f, concentrated set, scale, tower, weak Lindel{\"o}f number",

author = "Rodrigo Hern{\'a}ndez-Guti{\'e}rrez and Santi Spadaro",

note = "Publisher Copyright: {\textcopyright}2025 American Mathematical Society.",

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doi = "10.1090/proc/17224",

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T1 - CONSISTENCY AND INDEPENDENCE PHENOMENA INVOLVING CELLULAR-LINDELÖF SPACES

AU - Hernández-Gutiérrez, Rodrigo

AU - Spadaro, Santi

PY - 2025/6/1

Y1 - 2025/6/1

N2 - The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro [Monatsh. Math. 186 (2018), pp. 345–353]. We solve two questions of Alas, Gutiérrez-Domínguez and Wilson [Acta Math. Hungar. 167 (2022), pp 548–560] 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 almost cellular-Lindelöf property and normality are undetermined in ZFC.

AB - The cellular-Lindelöf property is a common generalization of the Lindelöf property and the countable chain condition that was introduced by Bella and Spadaro [Monatsh. Math. 186 (2018), pp. 345–353]. We solve two questions of Alas, Gutiérrez-Domínguez and Wilson [Acta Math. Hungar. 167 (2022), pp 548–560] 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 almost cellular-Lindelöf property and normality are undetermined in ZFC.

KW - Cellular-Lindelöf

KW - concentrated set

KW - scale

KW - tower

KW - weak Lindelöf number

UR - https://www.scopus.com/pages/publications/105006622752

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M3 - Article

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VL - 153

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JF - Proceedings of the American Mathematical Society

IS - 6

ER -

CONSISTENCY AND INDEPENDENCE PHENOMENA INVOLVING CELLULAR-LINDELÖF SPACES

Abstract

Keywords

ASJC Scopus subject areas

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