{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:18:18Z","timestamp":1773145098445,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its $d$-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower semicontinuous $\\bar{\\mathbb{R}}_+$-valued function is the supremum of a chain of Lipschitz Yoneda-continuous maps; the continuous Yoneda-complete quasi-metric spaces are exactly the retracts of algebraic Yoneda-complete quasi-metric spaces; every continuous Yoneda-complete quasi-metric space has a so-called quasi-ideal model, generalizing a construction due to K. Martin. The point is that all those results reduce to domain-theoretic constructions on posets of formal balls.<\/jats:p>","DOI":"10.23638\/lmcs-13(4:18)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:21Z","timestamp":1743701301000},"source":"Crossref","is-referenced-by-count":1,"title":["A Few Notes on Formal Balls"],"prefix":"10.23638","volume":"Volume 13, Issue 4","author":[{"given":"Jean","family":"Goubault-Larrecq","sequence":"first","affiliation":[]},{"given":"Kok Min","family":"Ng","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,11,28]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1606.05445v6","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1606.05445v6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:21Z","timestamp":1743701301000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,28]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(4:18)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1606.05445v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1606.05445v1","asserted-by":"subject"}],"has-review":[{"id-type":"uri","id":"https:\/\/zbmath.org\/6816940","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1606.05445","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1606.05445","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,28]]},"article-number":"2021"}}