{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:35:44Z","timestamp":1753889744276,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T00:00:00Z","timestamp":1427241600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We begin to study classical dimension theory from the computable analysis\n(TTE) point of view. For computable metric spaces, several effectivisations of\nzero-dimensionality are shown to be equivalent. The part of this\ncharacterisation that concerns covering dimension extends to higher dimensions\nand to closed shrinkings of finite open covers. To deal with zero-dimensional\nsubspaces uniformly, four operations (relative to the space and a class of\nsubspaces) are defined; these correspond to definitions of inductive and\ncovering dimensions and a countable basis condition. Finally, an effective\nretract characterisation of zero-dimensionality is proven under an effective\ncompactness condition. In one direction this uses a version of the construction\nof bilocated sets.<\/jats:p>","DOI":"10.2168\/lmcs-11(1:11)2015","type":"journal-article","created":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T07:33:27Z","timestamp":1431934407000},"source":"Crossref","is-referenced-by-count":0,"title":["Effective zero-dimensionality for computable metric spaces"],"prefix":"10.46298","volume":"Volume 11, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0142-867X","authenticated-orcid":false,"given":"Robert","family":"Kenny","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,3,25]]},"reference":[{"key":"931:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1023\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:01:28Z","timestamp":1681243288000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,25]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(1:11)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1501.03783","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1501.03783","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,3,25]]},"article-number":"1023"}}