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 | Size | Format | |
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TIA-282-107316.pdf | 490.35 kB | Adobe PDF | View/Open |
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