{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T15:17:14Z","timestamp":1693581434540},"reference-count":13,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2012,7,6]],"date-time":"2012-07-06T00:00:00Z","timestamp":1341532800000},"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":[[2012,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>A<\/jats:italic> be a subset of the constructive real line. What are the necessary and sufficient conditions for the set <jats:italic>A<\/jats:italic> such that <jats:italic>A<\/jats:italic> is continuously separated from other reals, i.e., there exists a continuous function <jats:italic>f<\/jats:italic> with <jats:italic>f<\/jats:italic><jats:sup>\u22121<\/jats:sup>(0) = <jats:italic>A<\/jats:italic>? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics.<\/jats:p>","DOI":"10.1002\/malq.201110040","type":"journal-article","created":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T18:27:13Z","timestamp":1344018433000},"page":"348-355","source":"Crossref","is-referenced-by-count":0,"title":["On the constructive notion of closure maps"],"prefix":"10.1002","volume":"58","author":[{"given":"Mohammad","family":"Ardeshir","sequence":"first","affiliation":[]},{"given":"Rasoul","family":"Ramezanian","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,6]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710094"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.06.005"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-3577(07)00012-2"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-007-0063-1"},{"key":"e_1_2_6_6_1","first-page":"3160","article-title":"Rearranging Series Constructively","volume":"15","author":"Berger J.","year":"2009","journal-title":"J. Univers. Comput. Sci"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0131-9"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610006"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0189-4"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.018"},{"key":"e_1_2_6_11_1","volume-title":"Constructivism in Mathematics, Vol. I, An introduction, Studies in Logic and the Foundations of Mathematics Vol. 121","author":"Troelstra A. S.","year":"1988"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90029-3"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85108-0"},{"key":"e_1_2_6_14_1","first-page":"2142","article-title":"Perhaps the intermediate value theorem","volume":"11","author":"Veldman W.","year":"2005","journal-title":"J. Univers. Comput. Sci"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201110040","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201110040","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201110040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T03:38:55Z","timestamp":1693453135000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201110040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,6]]},"references-count":13,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1002\/malq.201110040"],"URL":"https:\/\/doi.org\/10.1002\/malq.201110040","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7,6]]}}}