{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:25:15Z","timestamp":1785403515064,"version":"3.56.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"unspecified","delay-in-days":144,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2026]]},"abstract":"Abstract<\/jats:title>\n \n We first introduce and investigate a new class of\n \n \n \n $T_0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -spaces \u2013 strong\n \n \n \n $R$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -spaces, which are stronger than both\n \n \n \n $R$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -spaces and strongly well-filtered spaces. It is proved that any sup-complete poset equipped with the upper topology is a strong\n \n \n \n $R$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -space, and the Hoare power space of a\n \n \n \n $T_0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -space is a strong\n \n \n \n $R$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -space. Hence, the upper topology on a sup-complete poset is strongly well-filtered, and the Hoare power space of a\n \n \n \n $T_0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -space is strongly well-filtered, which answers two problems recently posed by Xu.\n <\/jats:p>","DOI":"10.1017\/s0960129526100589","type":"journal-article","created":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T07:15:21Z","timestamp":1779693321000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Strong well-filteredness of upper topology on sup-complete posets"],"prefix":"10.1017","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1159-8477","authenticated-orcid":false,"given":"Xiaoquan","family":"Xu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05nkgk822","id-type":"ROR","asserted-by":"publisher"}],"name":"Jiangxi Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05nkgk822","id-type":"ROR","asserted-by":"publisher"}],"name":"Jiangxi Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lizi","family":"Chen","sequence":"additional","affiliation":[{"name":"Minnan Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,5,25]]},"reference":[{"key":"S0960129526100589_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(78)90048-X"},{"key":"S0960129526100589_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2024.108973"},{"key":"S0960129526100589_ref20","unstructured":"Schalk, A. (1993). Algebras for generalized power constructions. Phd thesis, Technische Hochschule Darmstadt."},{"key":"S0960129526100589_ref10","unstructured":"Jia, X. (2018). Meet-continuity and locally compact sober Dcpos. Phd thesis, University of Birmingham."},{"key":"S0960129526100589_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2020.107323"},{"key":"S0960129526100589_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2021.107667"},{"key":"S0960129526100589_ref2","volume-title":"General Topology","author":"Engelking","year":"1989"},{"key":"S0960129526100589_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194315"},{"key":"S0960129526100589_ref11","volume-title":"Cartesian Closed Categories of Domains","author":"Jung","year":"1989"},{"key":"S0960129526100589_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2020.107540"},{"key":"S0960129526100589_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139524438"},{"key":"S0960129526100589_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2017.08.049"},{"key":"S0960129526100589_ref6","unstructured":"Heckmann, R. (1990). Power domain constructions. Phd thesis, Universit\u00e4t des Saarlandes."},{"key":"S0960129526100589_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725"},{"key":"S0960129526100589_ref19","first-page":"305C307","volume-title":"General Topology and Modern Analysis","author":"Rudin","year":"1980"},{"key":"S0960129526100589_ref4","first-page":"191","article-title":"Quasicontinuous posets","volume":"9","author":"Gierz","year":"1983","journal-title":"Houston Journal of Mathematics"},{"key":"S0960129526100589_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10473-023-0401-3"},{"key":"S0960129526100589_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129524000240"},{"key":"S0960129526100589_ref7","first-page":"272","volume-title":"An Upper Power Domain Construction in Terms of Strongly Compact Sets","author":"Heckmann","year":"1992"},{"key":"S0960129526100589_ref1","first-page":"1","volume-title":"Semantic Structures, Handbook of Logic in Computer Science","author":"Abramsky","year":"1994"},{"key":"S0960129526100589_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2013.09.015"},{"key":"S0960129526100589_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089911"},{"key":"S0960129526100589_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.06.019"},{"key":"S0960129526100589_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2018.10.003"},{"key":"S0960129526100589_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089920"},{"key":"S0960129526100589_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2020.107080"},{"key":"S0960129526100589_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2025.109654"},{"key":"S0960129526100589_ref24","volume-title":"Order and Topology","author":"Xu","year":"2016"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129526100589","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T07:15:23Z","timestamp":1779693323000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129526100589\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":28,"alternative-id":["S0960129526100589"],"URL":"https:\/\/doi.org\/10.1017\/s0960129526100589","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}],"article-number":"e19"}}