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

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