{"docId":4100,"paperId":2021,"url":"https:\/\/lmcs.episciences.org\/2021","doi":"10.23638\/LMCS-13(4:18)2017","journalName":"Logical Methods in Computer Science","issn":"","eissn":"1860-5974","volume":[{"vid":315,"name":"Volume 13, Issue 4"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1606.05445","repositoryVersion":6,"repositoryLink":"https:\/\/arxiv.org\/abs\/1606.05445v6","dateSubmitted":"2016-09-06 10:05:07","dateAccepted":"2017-11-28 17:30:56","datePublished":"2017-11-28 17:34:03","titles":["A Few Notes on Formal Balls"],"authors":["Goubault-Larrecq, Jean","Ng, Kok Min"],"abstracts":["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."],"keywords":["Mathematics - General Topology","54E99"]}