{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:34:46Z","timestamp":1753889686201,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,4,27]],"date-time":"2017-04-27T00:00:00Z","timestamp":1493251200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We introduce Z-stability, a notion capturing the intuition that if a function\nf maps a metric space into a normed space and if the norm of f(x) is small,\nthen x is close to a zero of f. Working in Bishop's constructive setting, we\nfirst study pointwise versions of Z-stability and the related notion of good\nbehaviour for functions. We then present a recursive counterexample to the\nclassical argument for passing from pointwise Z-stability to a uniform version\non compact metric spaces. In order to effect this passage constructively, we\nbring into play the positivity principle, equivalent to Brouwer's fan theorem\nfor detachable bars, and the limited anti-Specker property, an intuitionistic\ncounterpart to sequential compactness. The final section deals with connections\nbetween the limited anti-Specker property, positivity properties, and\n(potentially) Brouwer's fan theorem for detachable bars.<\/jats:p>","DOI":"10.2168\/lmcs-12(3:10)2016","type":"journal-article","created":{"date-parts":[[2017,8,10]],"date-time":"2017-08-10T10:03:42Z","timestamp":1502359422000},"source":"Crossref","is-referenced-by-count":0,"title":["Z-stability in Constructive Analysis"],"prefix":"10.46298","volume":"Volume 12, Issue 3","author":[{"given":"Douglas","family":"Bridges","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Dent","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maarten","family":"McKubre-Jordens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2017,4,27]]},"reference":[{"key":"1251:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/2031\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/2031\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:09:07Z","timestamp":1681243747000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/2031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,27]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-12(3:10)2016","relation":{"is-same-as":[{"id-type":"arxiv","id":"1602.07368","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1602.07368","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,4,27]]},"article-number":"2031"}}