{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T11:10:54Z","timestamp":1770894654981,"version":"3.50.1"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T00:00:00Z","timestamp":1679616000000},"content-version":"unspecified","delay-in-days":82,"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":[[2023,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we study quasi-metric spaces using domain theory. Given a quasi-metric space (<jats:italic>X<\/jats:italic>,<jats:italic>d<\/jats:italic>), we use <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129523000105_inline1.png\"\/><jats:tex-math>\n$({\\bf B}(X,d),\\leq^{d^{+}}\\!)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> to denote the poset of formal balls of the associated quasi-metric space (<jats:italic>X<\/jats:italic>,<jats:italic>d<\/jats:italic>). We introduce the notion of local Yoneda-complete quasi-metric spaces in terms of domain-theoretic properties of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129523000105_inline2.png\"\/><jats:tex-math>\n$({\\bf B}(X,d),\\leq^{d^{+}}\\!)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. The manner in which this definition is obtained is inspired by Romaguera\u2013Valero theorem and Kostanek\u2013Waszkiewicz theorem. Furthermore, we obtain characterizations of local Yoneda-complete quasi-metric spaces via local nets in quasi-metric spaces. More precisely, we prove that a quasi-metric space is local Yoneda-complete if and only if every local net has a <jats:italic>d<\/jats:italic>-limit. Finally, we prove that every quasi-metric space has a local Yoneda completion.<\/jats:p>","DOI":"10.1017\/s0960129523000105","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:28:11Z","timestamp":1679653691000},"page":"33-45","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["Local Yoneda completions of quasi-metric spaces"],"prefix":"10.1017","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3467-9299","authenticated-orcid":false,"given":"Jing","family":"Lu","sequence":"first","affiliation":[]},{"given":"Bin","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,3,24]]},"reference":[{"key":"S0960129523000105_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725"},{"key":"S0960129523000105_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00243-5"},{"key":"S0960129523000105_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129510000447"},{"key":"S0960129523000105_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02924844"},{"key":"S0960129523000105_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(81)90027-X"},{"key":"S0960129523000105_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(04)80085-9"},{"key":"S0960129523000105_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129510000010"},{"key":"S0960129523000105_ref1","volume-title":"Handbook of Logic in Computer Science","author":"Abramsky","year":"1994"},{"key":"S0960129523000105_ref7","first-page":"1","article-title":"A few notes on formal balls","volume":"13","author":"Goubault-Larrecq","year":"2017","journal-title":"Logical Methods in Computer Science"},{"key":"S0960129523000105_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00042-X"},{"key":"S0960129523000105_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2017.08.009"},{"key":"S0960129523000105_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00335-2"},{"key":"S0960129523000105_ref6","volume-title":"New Mathematical Monographs","author":"Goubault-Larrecq","year":"2013"},{"key":"S0960129523000105_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2019.07.024"},{"key":"S0960129523000105_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-19020-1_12"},{"key":"S0960129523000105_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129509007439"},{"key":"S0960129523000105_ref16","first-page":"328","article-title":"Localic completion of generalized metric spaces I","volume":"14","author":"Vickers","year":"2005","journal-title":"Theory and Applications of categories"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129523000105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T09:12:11Z","timestamp":1683191531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129523000105\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["S0960129523000105"],"URL":"https:\/\/doi.org\/10.1017\/s0960129523000105","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}