{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:37:11Z","timestamp":1758476231547,"version":"3.37.3"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"5","funder":[{"name":"Ministry of Economy and Competitiveness of Spain","award":["MTM2012-37894-C02-02"],"award-info":[{"award-number":["MTM2012-37894-C02-02"]}]},{"DOI":"10.13039\/501100003451","name":"UPV\/EHU","doi-asserted-by":"crossref","award":["UFI11\/52"],"award-info":[{"award-number":["UFI11\/52"]}],"id":[{"id":"10.13039\/501100003451","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003451","name":"UPV\/EHU","doi-asserted-by":"crossref","award":["GIU12\/39"],"award-info":[{"award-number":["GIU12\/39"]}],"id":[{"id":"10.13039\/501100003451","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Centre for Mathematics of the University of Coimbra","award":["PEst-C\/MAT\/UI0324\/2011"],"award-info":[{"award-number":["PEst-C\/MAT\/UI0324\/2011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper introduces the frame of partially defined real numbers and the lattice-ordered ring of partial real functions on a frame. This is then used to construct the order completion of rings of pointfree continuous real functions. The bounded and integer-valued cases are also analysed. The application of this pointfree approach to the classical case C(<jats:italic>X<\/jats:italic>) of the ring of continuous real-valued functions on a topological space <jats:italic>X<\/jats:italic> yields a new construction for the Dedekind completion of C(<jats:italic>X<\/jats:italic>), considerably more direct and natural than the known procedure using Hausdorff continuous functions.<\/jats:p>","DOI":"10.1515\/forum-2012-0095","type":"journal-article","created":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T03:09:19Z","timestamp":1381892959000},"page":"2551-2585","source":"Crossref","is-referenced-by-count":6,"title":["On the Dedekind completion of function rings"],"prefix":"10.1515","volume":"27","author":[{"given":"Imanol","family":"Mozo Carollo","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Basque Country UPV\/EHU, Apdo. 644, 48080 Bilbao, Spain"}]},{"given":"Javier","family":"Guti\u00e9rrez Garc\u00eda","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Basque Country UPV\/EHU, Apdo. 644, 48080 Bilbao, Spain"}]},{"given":"Jorge","family":"Picado","sequence":"additional","affiliation":[{"name":"CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal"}]}],"member":"374","published-online":{"date-parts":[[2013,10,16]]},"container-title":["Forum Mathematicum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2012-0095\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2012-0095\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:24:19Z","timestamp":1680301459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2012-0095\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,16]]},"references-count":0,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2014,1,10]]},"published-print":{"date-parts":[[2015,9,1]]}},"alternative-id":["10.1515\/forum-2012-0095"],"URL":"https:\/\/doi.org\/10.1515\/forum-2012-0095","relation":{},"ISSN":["0933-7741","1435-5337"],"issn-type":[{"type":"print","value":"0933-7741"},{"type":"electronic","value":"1435-5337"}],"subject":[],"published":{"date-parts":[[2013,10,16]]}}}