Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/22245
Title: 
Authors: 
Subjects: 
Sober space
Co-sober space
Poset model
Dcpo model
Issue Date: 
2020
Citation: 
Shen, C., Wu, G., Xi, X., & Zhao, D. (2020). Sober Scott spaces are not always co-sober. Topology and its Applications, 282, Article 107316. https://doi.org/10.1016/j.topol.2020.107316
Abstract: 
A nonempty compact saturated subset F of a topological space is called k-irreducible if it cannot be written as a union of two compact saturated proper subsets. A topological space is said to be co-sober if each of its k-irreducible compact saturated sets is the saturation of a point. Wen and Xu (2018) proved that Isbell's non-sober complete lattice equipped with the lower topology is sober but not co-sober. So far, it is still unknown whether every sober Scott space is co-sober. In this paper, we construct a dcpo whose Scott space is sober but not co-sober, which strengthens Wen and Xu's result.
Description: 
This is the final draft, after peer-review, of a manuscript published in Topology and its Applications. The published version is available online at https://doi.org/10.1016/j.topol.2020.107316
URI: 
ISSN: 
0166-8641
DOI: 
File Permission: 
Open
File Availability: 
With file
Appears in Collections:Journal Articles

Files in This Item:
File Description SizeFormat 
TIA-282-107316.pdf490.35 kBAdobe PDFThumbnail
View/Open
Show full item record

SCOPUSTM   
Citations

1
checked on Mar 25, 2023

Page view(s)

69
checked on Mar 30, 2023

Download(s)

17
checked on Mar 30, 2023

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.