{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:39:35Z","timestamp":1753889975205,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,4,27]],"date-time":"2017-04-27T00:00:00Z","timestamp":1493251200000},"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>When given a class of functions and a finite collection of sets, one might be\ninterested whether the class in question contains any function whose domain is\na subset of the union of the sets of the given collection and whose\nrestrictions to all of them belong to this class. The collections with the\nformulated property are said to be strongly join permitting for the given class\n(the notion of join permitting collection is defined in the same way, but\nwithout the words \"a subset of\"). Three theorems concerning certain instances\nof the problem are proved. A necessary and sufficient condition for being\nstrongly join permitting is given for the case when, for some $n$, the class\nconsists of the potentially partial recursive functions of $n$ variables, and\nthe collection consists of sets of $n$-tuples of natural numbers. The second\ntheorem gives a sufficient condition for the case when the class consists of\nthe continuous partial functions between two given topological spaces, and the\ncollection consists of subsets of the first of them (the condition is also\nnecessary under a weak assumption on the second one). The third theorem is of a\nsimilar character but, instead of continuity, it concerns computability in the\nspirit of the one in effective topological spaces.<\/jats:p>","DOI":"10.2168\/lmcs-12(4:3)2016","type":"journal-article","created":{"date-parts":[[2017,8,10]],"date-time":"2017-08-10T10:07:20Z","timestamp":1502359640000},"source":"Crossref","is-referenced-by-count":0,"title":["Some theorems on passing from local to global presence of properties of functions"],"prefix":"10.46298","volume":"Volume 12, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5718-3640","authenticated-orcid":false,"given":"Dimiter","family":"Skordev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2017,4,27]]},"reference":[{"key":"1200:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/2169\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/2169\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:09:22Z","timestamp":1681243762000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/2169"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,27]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-12(4:3)2016","relation":{"is-same-as":[{"id-type":"arxiv","id":"1609.04254","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1609.04254","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,4,27]]},"article-number":"2169"}}