{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T20:10:24Z","timestamp":1697659824417},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2004,11,25]],"date-time":"2004-11-25T00:00:00Z","timestamp":1101340800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove in the framework of Bishop's constructive mathematics that the sequential completion <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$ \\tilde {\\cal D} $\\end{document}<\/jats:styled-content>(\u211d) of the space \ud835\udc9f(\u211d) is filter\u2010complete. Then it follows as a corollary that the filter\u2010completeness of \ud835\udc9f(\u211d) is equivalent to the principle BD\u2010\u2115, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$ \\tilde {\\cal D} $\\end{document}<\/jats:styled-content>(\u211d) is identical with the filter\u2010completion which was provided by Bishop. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310128","type":"journal-article","created":{"date-parts":[[2004,11,25]],"date-time":"2004-11-25T08:46:56Z","timestamp":1101372416000},"page":"77-82","source":"Crossref","is-referenced-by-count":2,"title":["The constructive completion of the space \ud835\udc9f(\u211d)"],"prefix":"10.1002","volume":"51","author":[{"given":"Satoru","family":"Yoshida","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,11,25]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"E.Bishop Foundations of Constructive Analysis (McGraw\u2010Hill New York 1967)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"E.Bishop andD.Bridges Constructive Analysis (Springer\u2010Verlag Heidelberg et al. 1985).","DOI":"10.1007\/978-3-642-61667-9"},{"key":"e_1_2_1_4_2","unstructured":"D.Bridges Constructive Functional Analysis (Pitman London 1979)."},{"key":"e_1_2_1_5_2","unstructured":"D.Bridges H.Ishihara P.Schuster andL.V\u00ee\u0163\u0103 Strong continuity implies uniform sequential continuity. Preprint 2001."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275292"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150296"},{"key":"e_1_2_1_8_2","unstructured":"L.Schwartz The\u00f3rie des distributions. Nouvelle \u00e9dition (Hermann Paris 1966)."},{"key":"e_1_2_1_9_2","unstructured":"F.Traves Topological Vector Spaces Distributions and Kernels (Academic Press New York and London 1967)."},{"key":"e_1_2_1_10_2","unstructured":"A. S.Troelstra andD.van Dalen Constructivism in Mathematics Vol. 1 (North\u2010Holland Publ. Comp. Amsterdam 1988)."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310031"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310128","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310128","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T19:56:30Z","timestamp":1697658990000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,25]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,1]]}},"alternative-id":["10.1002\/malq.200310128"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310128","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,11,25]]}}}