When exactly is Scott sober?

Ho, Weng Kin; Zhao, Dongsheng

Publication:
When exactly is Scott sober?

cris.virtual.author-orcid	0000-0002-4585-9340
cris.virtual.author-orcid	0000-0001-8446-3624
cris.virtual.department	Mathematics & Mathematics Education (MME)
cris.virtual.department	Mathematics & Mathematics Education (MME)
cris.virtualsource.author-orcid	4f61f65b-2eb0-49d3-8ccc-fd5399070ae9
cris.virtualsource.author-orcid	04f740f5-f584-446d-a637-7c29677bfc31
cris.virtualsource.department	4f61f65b-2eb0-49d3-8ccc-fd5399070ae9
cris.virtualsource.department	04f740f5-f584-446d-a637-7c29677bfc31
dc.contributor.author	Ho, Weng Kin
dc.contributor.author	Zhao, Dongsheng
dc.date.accessioned	2014-07-02T06:03:44Z
dc.date.available	2014-07-02T06:03:44Z
dc.date.issued	2010
dc.description	Technical report M2010-02, September 2010, Mathematics and Mathematics Education, National Institute of Education, Singapore
dc.description.abstract	A topological space is sober if every nonempty irreducible closed set is the closure of a unique singleton set. Sobriety is precisely the topological property that allows one to recover completely a topological space from its frame of opens. Because every Hausdor space is sober, sobriety is an overt, and hence unnamed, notion. Even in non-Hausdor settings, sober spaces abound. A well-known instance of a sober space appears in domain theory: the Scott topology of a continuous dcpo is sober. The converse is false as witnessed by two counterexamples constructed in the early 1980's: the first by P.T. Johnstone and the second (a complete lattice) by J. Isbell. Since then, there has been limited progress in the quest for an order-theoretic characterization of those dcpo's for which their Scott topology is sober. This paper provides one answer to this open problem.	en
dc.identifier.citation	Ho, W. K., & Zhao, D. (2010). When exactly is Scott sober? (Report No. M2010-02). National Institute of Education (Singapore). NIE Digital Repository. https://hdl.handle.net/10497/15606	en
dc.identifier.uri	https://hdl.handle.net/10497/15606
dc.language.iso	en	en
dc.publisher	National Institute of Education (Singapore)	en
dc.rights	Copyright protected. Permission to publish required.
dc.subject	Scott topology	en
dc.subject	Sober space	en
dc.subject	dcpo	en
dc.subject	Dominated dcpo,	en
dc.subject	H-continuous	en
dc.subject	H-algebraic	en
dc.subject	H-compact	en
dc.subject	Strongly H-algebraic	en
dc.title	When exactly is Scott sober?	en
dc.type	Technical Report	en
dspace.entity.type	Publication
local.message.claim	2021-12-23T13:02:40.384+0800\|\|\|rp00120\|\|\|submit_approve\|\|\|dc_contributor_author\|\|\|None	*
local.message.claim	2021-12-23T13:11:28.869+0800\|\|\|rp00129\|\|\|submit_approve\|\|\|dc_contributor_author\|\|\|None	*