{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:59:56Z","timestamp":1758272396668},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4119,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120000918X_inline1\" \/>(\u211d) of test functions is equivalent to the principle BD-\u2115 which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.<\/jats:p>","DOI":"10.2178\/jsl\/1190150296","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:16:54Z","timestamp":1197555414000},"page":"1511-1519","source":"Crossref","is-referenced-by-count":11,"title":["A constructive look at the completeness of the space (\u211d)"],"prefix":"10.1017","volume":"67","author":[{"given":"Hajime","family":"Ishihara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Satoru","family":"Yoshida","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000918X_ref004","volume-title":"Strong continuity implies uniform sequential continuity","author":"Bridges","year":"2001"},{"key":"S002248120000918X_ref007","first-page":"5","volume-title":"Combinatorics, Computability and Logic, Proceedings of the Third International Conference on Combinatorics, Computability and Logic, (DMTCS'01) in Constan\u0163a Romania","author":"Ishihara"},{"key":"S002248120000918X_ref001","volume-title":"Foundations of Constructive Analysis","author":"Bishop","year":"1967"},{"key":"S002248120000918X_ref002","volume-title":"Grundlehren der Mathematischen Wissenschaften","volume":"279","author":"Bishop","year":"1985"},{"key":"S002248120000918X_ref003","volume-title":"Constructive Functional Analysis","author":"Bridges","year":"1979"},{"key":"S002248120000918X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0073966"},{"key":"S002248120000918X_ref006","first-page":"557","volume":"57","author":"Ishihara","year":"1992","journal-title":"Continuity properties in constructive mathematics"},{"key":"S002248120000918X_ref009","volume-title":"Constructivism in Mathematics","volume":"2","author":"Troelstra","year":"1988"},{"key":"S002248120000918X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000918X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:17:51Z","timestamp":1557173871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000918X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S002248120000918X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150296","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}