{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:33:51Z","timestamp":1761294831079,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["731143"],"award-info":[{"award-number":["731143"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>Within Bishop-style constructive mathematics we study the classical McShane-Whitney theorem on the extendability of real-valued Lipschitz functions defined on a subset of a metric space. Using a formulation similar to the formulation of McShane-Whitney theorem, we show that the Lipschitz real-valued functions on a totally bounded space are uniformly dense in the set of uniformly continuous functions. Through the introduced notion of a McShane-Whitney pair we describe the constructive content of the original McShane-Whitney extension and examine how the properties of a Lipschitz function defined on the subspace of the pair extend to its McShane-Whitney extensions on the space of the pair. Similar McShane-Whitney pairs and extensions are established for H\\&amp;quot;{o}lder functions and $\\nu$-continuous functions, where $\\nu$ is a modulus of continuity. A Lipschitz version of a fundamental corollary of the Hahn-Banach theorem, and the approximate McShane-Whitney theorem are shown.<\/jats:p>","DOI":"10.23638\/lmcs-16(1:18)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:23Z","timestamp":1743701843000},"source":"Crossref","is-referenced-by-count":1,"title":["McShane-Whitney extensions in constructive analysis"],"prefix":"10.23638","volume":"Volume 16, Issue 1","author":[{"given":"Iosif","family":"Petrakis","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,2,17]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1804.06757v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1804.06757v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:24Z","timestamp":1743701844000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,17]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(1:18)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1804.06757v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1804.06757v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1804.06757v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1804.06757","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1804.06757","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,2,17]]},"article-number":"4455"}}