Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/20434
Full metadata record
DC FieldValueLanguage
dc.contributor.authorZhao, Dongsheng-
dc.contributor.authorXi, Xiaoyong-
dc.date.accessioned2018-11-19T07:30:50Z-
dc.date.available2018-11-19T07:30:50Z-
dc.date.issued2018-
dc.identifier.citationZhao, D., & Xi, X. (2018). Directed complete poset models of T1 spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 164(1), 125-134. https://doi.org/10.1017/S0305004116000888en
dc.identifier.issn0305-0041 (print)-
dc.identifier.issn1469-8064 (online)-
dc.identifier.urihttp://hdl.handle.net/10497/20434-
dc.description.abstractA poset model of a topological space X is a poset P such that the subspace Max(P) of the Scott space P is homeomorphic to X, where Max(P) is the set of all maximal points of P. Every T1 space has a (bounded complete algebraic) poset model. It was, however, not known whether every T1 space has a directed complete poset model and whether every sober T1 space has a directed complete poset model whose Scott topology is sober. In this paper we give a positive answer to each of these two problems. For each T1 space X, we shall construct a directed complete poset E that is a model of X, and prove that X is sober if and only if the Scott space E is sober. One useful by-product is a method for constructing more directed complete posets whose Scott topology is not sober.en
dc.language.isoenen
dc.titleDirected complete poset models of T1 spacesen
dc.typeArticleen
dc.identifier.doi10.1017/S0305004116000888-
local.message.claim2021-12-23T13:11:28.869+0800|||rp00129|||submit_approve|||dc_contributor_author|||None*
item.openairetypeArticle-
item.cerifentitytypePublications-
item.languageiso639-1en-
item.fulltextWith file-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextOpen-
Appears in Collections:Journal Articles
Files in This Item:
File Description SizeFormat 
MPCPS-164-1-125.pdf368.35 kBAdobe PDFThumbnail
View/Open
Show simple item record

SCOPUSTM   
Citations

14
checked on Jul 3, 2022

WEB OF SCIENCETM
Citations

13
checked on Jul 3, 2022

Page view(s)

82
checked on Jul 6, 2022

Download(s) 50

96
checked on Jul 6, 2022

Google ScholarTM

Check

Altmetric


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