{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T06:11:11Z","timestamp":1697695871002},"reference-count":13,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T00:00:00Z","timestamp":1153699200000},"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":[[2006,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A metric space is said to be <jats:italic>locally non\u2010compact<\/jats:italic> if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non\u2010compact iff it is without isolated points.<\/jats:p><jats:p>The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence that is eventually computably bounded away from every computable element of the space. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510036","type":"journal-article","created":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T14:46:52Z","timestamp":1153752412000},"page":"323-330","source":"Crossref","is-referenced-by-count":0,"title":["On local non\u2010compactness in recursive mathematics"],"prefix":"10.1002","volume":"52","author":[{"given":"Jakob G.","family":"Simonsen","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,7,24]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"O.Aberth Computable Analysis (McGraw\u2010Hill 1980)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"E.Bishop andD.Bridges Constructive Analysis. Grundlehren der mathematischen Wissenschaften 279 (Springer 1985).","DOI":"10.1007\/978-3-642-61667-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"D.Bridges andF.Richman Varieties of Constructive Mathematics. London Mathematical Society Lecture Notes Series 97 (Cambridge University Press 1987).","DOI":"10.1017\/CBO9780511565663"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310104"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19730191901"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19750210164"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19770231902"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273473"},{"key":"e_1_2_1_10_2","unstructured":"H.RogersJr. Theory of Recursive Functions and Effective Computability (paperback edition) (The MIT Press 1987)."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2267043"},{"key":"e_1_2_1_12_2","unstructured":"A. S.Troelstra andD.van Dalen Constructivism in Mathematics: An Introduction. Studies in Logic and the Foundations of Mathematics 121 and 123 (North\u2010Holland 1987)."},{"key":"e_1_2_1_13_2","first-page":"41","article-title":"On singular coverings and properties of constructive functions connected with them","volume":"98","author":"Tseitin G. S.","year":"1962","journal-title":"American Mathematical Society Translations (Series 2)"},{"key":"e_1_2_1_14_2","unstructured":"K.Weihrauch Computable Analysis: An Introduction (Springer 1998)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510036","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T18:05:12Z","timestamp":1697652312000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,24]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,8]]}},"alternative-id":["10.1002\/malq.200510036"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510036","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7,24]]}}}