Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/23336
Title: 
Authors: 
Subjects: 
First-countability
Sober space
Well-filtered space
ω-Rudin space
ω-Well-filtered space
Countably directed set
Issue Date: 
2021
Citation: 
Xu, X., Shen, C., Xi, X., & Zhao, D. (2021). First-countability, ω-Rudin spaces and well-filtered determined spaces. Topology and its Applications, 300, Article 107775. https://doi.org/10.1016/j.topol.2021.107775
Journal: 
Topology and its Applications
Abstract: 
In this paper, we investigate some versions of d-space, well-filtered space and Rudin space concerning various countability properties. It is proved that every space with a first-countable sobrification is an ω-Rudin space and every first-countable space is well-filtered determined. Therefore, every ω-well-filtered space with a first-countable sobrification is sober. It is also shown that every irreducible closed subset in a first-countable ω-well-filtered space is countably directed, hence every first-countable ω*-well-filtered d-space is sober.
URI: 
ISSN: 
0166-8641
DOI: 
File Permission: 
Embargo_20230901
File Availability: 
With file
Appears in Collections:Journal Articles

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  Until 2023-09-01
442.49 kBAdobe PDFUnder embargo until Sep 01, 2023
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