{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T06:13:28Z","timestamp":1711606408244},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of<jats:bold>R<\/jats:bold>onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if<jats:italic>G<\/jats:italic>is a complete (metric) abelian group that is the range of a continuous isomorphism from<jats:bold>R<\/jats:bold>, then<jats:italic>G<\/jats:italic>is noncompact. A special case occurs when<jats:italic>G<\/jats:italic>satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective mappings are proved en route to the main theorem. A Brouwerian example shows that some of our results are the best possible in a constructive framework.<\/jats:p>","DOI":"10.2178\/jsl\/1278682208","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T13:30:45Z","timestamp":1278682245000},"page":"930-944","source":"Crossref","is-referenced-by-count":1,"title":["Continuous isomorphisms from<b>R<\/b>onto a complete abelian group"],"prefix":"10.1017","volume":"75","author":[{"given":"Douglas","family":"Bridges","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Hendtlass","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002462_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61667-9"},{"key":"S0022481200002462_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0897-3_5"},{"key":"S0022481200002462_ref006","volume-title":"Omniscience, sequential compactness, and the anti-Specker property","author":"Bridges","year":"2008"},{"key":"S0022481200002462_ref013","doi-asserted-by":"publisher","DOI":"10.1142\/4681"},{"key":"S0022481200002462_ref011","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198505242.001.0001","volume-title":"Elements of intuitionism","volume":"39","author":"Dummett","year":"2000"},{"key":"S0022481200002462_ref002","first-page":"195","article-title":"A fan-theoretic equivalent of the antithesis of Specker's theorem","volume":"18","author":"Berger","year":"2007","journal-title":"Koninklijke Nederlandse Akademie van Wetenschappen. 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