Cardinal invariants of cellular-Lindelöf spaces

Angelo Bella; Santi Spadaro

doi:10.1007/s13398-019-00660-1

Cardinal invariants of cellular-Lindelöf spaces

Angelo Bella, Santi Spadaro

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

10 Scopus citations

Abstract

A space X is said to be cellular-Lindelöf if for every cellular family U there is a Lindelöf subspace L of X which meets every element of U. Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular G_δ-diagonal has cardinality at most 2 ^c. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2 ^< ^c= c and that every normal cellular-Lindelöf space with a G_δ-diagonal of rank 2 has cardinality at most continuum.

Original language	English
Pages (from-to)	2805-2811
Number of pages	7
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	113
Issue number	3
DOIs	https://doi.org/10.1007/s13398-019-00660-1
State	Published - 1 Jul 2019
Externally published	Yes

Keywords

Arhangel’skii Theorem
Cardinal inequality
Ccc
Cellular-Lindelöf
Elementary submodel
Lindelöf

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

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10.1007/s13398-019-00660-1

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title = "Cardinal invariants of cellular-Lindel{\"o}f spaces",

abstract = "A space X is said to be cellular-Lindel{\"o}f if for every cellular family U there is a Lindel{\"o}f subspace L of X which meets every element of U. Cellular-Lindel{\"o}f spaces generalize both Lindel{\"o}f spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindel{\"o}f monotonically normal space is Lindel{\"o}f and that every cellular-Lindel{\"o}f space with a regular Gδ-diagonal has cardinality at most 2 c. We also prove that every normal cellular-Lindel{\"o}f first-countable space has cardinality at most continuum under 2 < c= c and that every normal cellular-Lindel{\"o}f space with a Gδ-diagonal of rank 2 has cardinality at most continuum.",

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author = "Angelo Bella and Santi Spadaro",

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doi = "10.1007/s13398-019-00660-1",

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AU - Spadaro, Santi

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AB - A space X is said to be cellular-Lindelöf if for every cellular family U there is a Lindelöf subspace L of X which meets every element of U. Cellular-Lindelöf spaces generalize both Lindelöf spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelöf monotonically normal space is Lindelöf and that every cellular-Lindelöf space with a regular Gδ-diagonal has cardinality at most 2 c. We also prove that every normal cellular-Lindelöf first-countable space has cardinality at most continuum under 2 < c= c and that every normal cellular-Lindelöf space with a Gδ-diagonal of rank 2 has cardinality at most continuum.

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KW - Cardinal inequality

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Cardinal invariants of cellular-Lindelöf spaces

Abstract

Keywords

ASJC Scopus subject areas

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