Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/23496
Full metadata record
DC FieldValueLanguage
dc.contributor.authorXu, Xiaoquanen
dc.contributor.authorXi, Xiaoyongen
dc.contributor.authorZhao, Dongshengen
dc.date.accessioned2021-11-30T09:27:40Z-
dc.date.available2021-11-30T09:27:40Z-
dc.date.issued2021-
dc.identifier.citationXu, X., Xi, X., & Zhao, D. (2021). A complete Heyting algebra whose Scott space is non-sober. Fundamenta Mathematicae, 252(3), 315-323. https://doi.org/10.4064/fm704-4-2020en
dc.identifier.issn0016-2736 (print)-
dc.identifier.issn1730-6329 (online)-
dc.identifier.urihttp://hdl.handle.net/10497/23496-
dc.description.abstractWe prove that (1) for any complete lattice 𝓛, the set 𝒟 (𝓛) of all non-empty saturated compact subsets of the Scott space of 𝓛 is a complete Heyting algebra (with the reverse inclusion order); and (2) if the Scott space of a complete lattice 𝓛 is non-sober, then the Scott space of 𝒟 (𝓛) is non-sober. Using these results and Isbell's example of a non-sober complete lattice, we deduce that there is a complete Heyting algebra whose Scott space is non-sober, thus giving an affirmative answer to a problem posed by Achim Jung. We also prove that 𝚊 𝒯₀ space is well-filtered iff its upper space (the set 𝒟 (𝓧) of all non-empty saturated compact subsets of X equipped with the upper Vietoris topology) is well-filtered, which answers another open problem.en
dc.language.isoenen
dc.relation.ispartofFundamenta Mathematicaeen
dc.subjectScott topologyen
dc.subjectSober spaceen
dc.subjectWell-filtered spaceen
dc.subjectUpper spaceen
dc.titleA complete Heyting algebra whose Scott space is non-soberen
dc.typeArticleen
dc.description.versionAccepted versionen
dc.description.projectRI 3/16 ZDS-
dc.identifier.doi10.4064/fm704-4-2020-
dc.grant.idNSFC(11661057)en
dc.grant.id20161BAB2061004en
dc.grant.id20192ACBL20045en
dc.grant.idNSFC (11361028)en
dc.grant.idNSFC (61300153)en
dc.grant.idNSFC (11671008)en
dc.grant.idNSFC (11701500)en
dc.grant.idNSFC (11626207)en
dc.grant.idBK20170483en
dc.grant.fundingagencyNational Natural Science Foundation of Chinaen
dc.grant.fundingagencyNational Institute of Education, Singaporeen
local.message.claim2021-12-23T13:11:28.869+0800|||rp00129|||submit_approve|||dc_contributor_author|||None*
item.openairetypeArticle-
item.fulltextWith file-
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.languageiso639-1en-
item.grantfulltextOpen-
Appears in Collections:Journal Articles
Files in This Item:
File Description SizeFormat 
FM-252-315.pdf301.61 kBAdobe PDFThumbnail
View/Open
Show simple item record

SCOPUSTM   
Citations

9
checked on Aug 5, 2022

WEB OF SCIENCETM
Citations

8
checked on Aug 9, 2022

Page view(s)

59
checked on Aug 9, 2022

Download(s)

16
checked on Aug 9, 2022

Google ScholarTM

Check

Altmetric


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