{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T00:10:19Z","timestamp":1726445419517},"reference-count":22,"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":12520,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space<jats:italic>X<\/jats:italic>. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in<jats:italic>X<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273299","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:51:21Z","timestamp":1146952281000},"page":"609-625","source":"Crossref","is-referenced-by-count":17,"title":["Recursive constructions in topological spaces"],"prefix":"10.1017","volume":"44","author":[{"given":"Iraj","family":"Kalantari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allen","family":"Retzlaff","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"volume-title":"Constructivity in mathematics","year":"1959","author":"Specker","key":"S0022481200048489_ref022"},{"volume-title":"Annals of Mathematical Studies","year":"1966","author":"Sacks","key":"S0022481200048489_ref021"},{"volume-title":"Theory of recursive functions and effective computabiliiy","year":"1968","author":"Rogers","key":"S0022481200048489_ref020"},{"volume-title":"Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik","author":"Retzlaff","key":"S0022481200048489_ref019"},{"key":"S0022481200048489_ref017","unstructured":"Remmel J. , On r.e. and \u03c9-r.e. vector spaces with nonextendible bases, this Journal (to appear)."},{"key":"S0022481200048489_ref016","first-page":"341","article-title":"Computable algebra, general theory and theory of computable fields","volume":"95","author":"Rabin","year":"1960","journal-title":"Transactions of the American Mathematical 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topological spaces (forthcoming)."},{"key":"S0022481200048489_ref005","first-page":"481","volume":"42","author":"Kalantari","year":"1977","journal-title":"Maximal vector spaces under automorphisms of the lattice of recursively enumerable vector spaces"},{"key":"S0022481200048489_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19790252502"},{"key":"S0022481200048489_ref010","first-page":"129","volume-title":"Constructivity in mathematics","author":"Lacombe","year":"1959"},{"key":"S0022481200048489_ref018","first-page":"260","volume":"43","author":"Retzlaff","year":"1978","journal-title":"Simple and hyperhypersimple vector 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London"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048489","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T14:17:29Z","timestamp":1586873849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048489\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["S0022481200048489"],"URL":"https:\/\/doi.org\/10.2307\/2273299","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"type":"print","value":"0022-4812"},{"type":"electronic","value":"1943-5886"}],"subject":[],"published":{"date-parts":[[1979,12]]}}}