On totally Lindelöf spaces

Gabriel Fernandes; Guilherme Pinto; Vinicius Rocha

doi:10.1016/j.topol.2023.108704

On totally Lindelöf spaces

Gabriel Fernandes
, Guilherme Pinto
, Vinicius Rocha

Universidade de São Paulo

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

1 Scopus citations

Abstract

The results in this paper answer three questions asked by Noble in [10] and give a partial answer to a question asked by Alster in [1]. We prove that every Alster space is totally Lindelöf and this gives a new characterization of regular Alster spaces. We construct a non-regular totally Lindelöf space that is not Alster and we prove that there exists a Lindelöf P-space that is not Frolík.

Original language	English
Article number	108704
Journal	Topology and its Applications
Volume	341
DOIs	https://doi.org/10.1016/j.topol.2023.108704
State	Published - 1 Jan 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Funding

The author is funded by CAPES-88887.907521/2023-00.

Keywords

Alster spaces
Filter bases
Frolík spaces
Totally Lindelöf

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10.1016/j.topol.2023.108704

Cite this

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title = "On totally Lindel{\"o}f spaces",

abstract = "The results in this paper answer three questions asked by Noble in [10] and give a partial answer to a question asked by Alster in [1]. We prove that every Alster space is totally Lindel{\"o}f and this gives a new characterization of regular Alster spaces. We construct a non-regular totally Lindel{\"o}f space that is not Alster and we prove that there exists a Lindel{\"o}f P-space that is not Frol{\'i}k.",

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AU - Rocha, Vinicius

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N2 - The results in this paper answer three questions asked by Noble in [10] and give a partial answer to a question asked by Alster in [1]. We prove that every Alster space is totally Lindelöf and this gives a new characterization of regular Alster spaces. We construct a non-regular totally Lindelöf space that is not Alster and we prove that there exists a Lindelöf P-space that is not Frolík.

AB - The results in this paper answer three questions asked by Noble in [10] and give a partial answer to a question asked by Alster in [1]. We prove that every Alster space is totally Lindelöf and this gives a new characterization of regular Alster spaces. We construct a non-regular totally Lindelöf space that is not Alster and we prove that there exists a Lindelöf P-space that is not Frolík.

KW - Alster spaces

KW - Filter bases

KW - Frolík spaces

KW - Totally Lindelöf

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On totally Lindelöf spaces

Abstract

Bibliographical note

Funding

Keywords

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