{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T21:57:35Z","timestamp":1747173455004,"version":"3.40.5"},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"unspecified","delay-in-days":64,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system\u2019s state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust analyses cannot discriminate between a subset of the metric space and its closure; therefore, one can restrict to the complete lattice of closed subsets. When the metric space is compact, the complete lattice of closed subsets ordered by reverse inclusion is <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129523000233_inline1.png\"\/><jats:tex-math>\n$\\omega$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-continuous, and robust analyses are exactly the Scott-continuous maps. Thus, one can also ask whether a robust analysis is computable (with respect to a countable base). The main result of this paper establishes a relation between robustness and Scott continuity when the metric space is not compact. The key idea is to replace the metric space with a compact Hausdorff space, and relate robustness and Scott continuity by an adjunction between the complete lattice of closed subsets of the metric space and the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129523000233_inline2.png\"\/><jats:tex-math>\n$\\omega$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-continuous lattice of closed subsets of the compact Hausdorff space. We demonstrate the applicability of this result with several examples involving Banach spaces.<\/jats:p>","DOI":"10.1017\/s0960129523000233","type":"journal-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T08:04:15Z","timestamp":1691136255000},"page":"536-572","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Robustness, Scott continuity, and computability"],"prefix":"10.1017","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1879-0763","authenticated-orcid":false,"given":"Amin","family":"Farjudian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8018-6543","authenticated-orcid":false,"given":"Eugenio","family":"Moggi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"S0960129523000233_ref1","unstructured":"Abramsky, S. and Jung, A. (1994). Domain theory. In Abramsky, S. , Gabbay, D. M. and Maibaum, T. S. E. , editors, Handbook of Logic in Computer Science, vol. 3, pp. 1\u2013168. Clarendon Press."},{"volume-title":"Topics in Banach Space Theory","year":"2006","author":"Albiac","key":"S0960129523000233_ref2"},{"volume-title":"Topological Vector Spaces","year":"2011","author":"Narici","key":"S0960129523000233_ref21"},{"key":"S0960129523000233_ref6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1966-0199669-9"},{"key":"S0960129523000233_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-78499-9_5"},{"key":"S0960129523000233_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.06.020"},{"key":"S0960129523000233_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500004181"},{"key":"S0960129523000233_ref13","doi-asserted-by":"crossref","unstructured":"Gierz, G. , Hofmann, K. H. , Keimel, K. , Lawson, J. D. , Mislove, M. W. and Scott, D. S. (2003). Continuous Lattices and Domains, vol. 93. Encycloedia of Mathematics and its Applications. Cambridge University Press.","DOI":"10.1017\/CBO9780511542725"},{"key":"S0960129523000233_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129597002338"},{"key":"S0960129523000233_ref7","doi-asserted-by":"publisher","DOI":"10.1145\/234528.234740"},{"key":"S0960129523000233_ref11","doi-asserted-by":"crossref","unstructured":"Fr\u00e4nzle, M. (1999). Analysis of hybrid systems: An ounce of realism can save an infinity of states. In Computer Science Logic: 13th International Workshop, CSL\u201999 8th Annual Conference of the EACSL Madrid, Spain, September 20\u201325, 1999 Proceedings 13. Springer, 126\u2013139.","DOI":"10.1007\/3-540-48168-0_10"},{"key":"S0960129523000233_ref9","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1995.1096"},{"volume-title":"Topology","year":"2000","author":"Munkres","key":"S0960129523000233_ref20"},{"volume-title":"Functional Analysis","year":"1991","author":"Rudin","key":"S0960129523000233_ref22"},{"key":"S0960129523000233_ref8","doi-asserted-by":"publisher","DOI":"10.1145\/512950.512973"},{"year":"1980","author":"Gierz","key":"S0960129523000233_ref12"},{"key":"S0960129523000233_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000677"},{"volume-title":"Handbook of Categorical Algebra: Volume 1, Basic Category Theory","year":"1994","author":"Borceux","key":"S0960129523000233_ref3"},{"key":"S0960129523000233_ref14","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2008.931718"},{"key":"S0960129523000233_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-70914-7"},{"key":"S0960129523000233_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-22348-9_4"},{"volume-title":"A Course in Functional Analysis","year":"1990","author":"Conway","key":"S0960129523000233_ref5"},{"key":"S0960129523000233_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(77)90045-7"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129523000233","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T02:32:34Z","timestamp":1695004354000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129523000233\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["S0960129523000233"],"URL":"https:\/\/doi.org\/10.1017\/s0960129523000233","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"type":"print","value":"0960-1295"},{"type":"electronic","value":"1469-8072"}],"subject":[],"published":{"date-parts":[[2023,6]]},"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"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}