{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:35:32Z","timestamp":1753889732073,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,11,20]],"date-time":"2013-11-20T00:00:00Z","timestamp":1384905600000},"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>A notable feature of the TTE approach to computability is the representation\nof the argument values and the corresponding function values by means of\ninfinitistic names. Two ways to eliminate the using of such names in certain\ncases are indicated in the paper. The first one is intended for the case of\ntopological spaces with selected indexed denumerable bases. Suppose a partial\nfunction is given from one such space into another one whose selected base has\na recursively enumerable index set, and suppose that the intersection of base\nopen sets in the first space is computable in the sense of Weihrauch-Grubba.\nThen the ordinary TTE computability of the function is characterized by the\nexistence of an appropriate recursively enumerable relation between indices of\nbase sets containing the argument value and indices of base sets containing the\ncorresponding function value.This result can be regarded as an improvement of a\nresult of Korovina and Kudinov. The second way is applicable to metric spaces\nwith selected indexed denumerable dense subsets. If a partial function is given\nfrom one such space into another one, then, under a semi-computability\nassumption concerning these spaces, the ordinary TTE computability of the\nfunction is characterized by the existence of an appropriate recursively\nenumerable set of quadruples. Any of them consists of an index of element from\nthe selected dense subset in the first space, a natural number encoding a\nrational bound for the distance between this element and the argument value, an\nindex of element from the selected dense subset in the second space and a\nnatural number encoding a rational bound for the distance between this element\nand the function value. One of the examples in the paper indicates that the\ncomputability of real functions can be characterized in a simple way by using\nthe first way of elimination of the infinitistic names.<\/jats:p>","DOI":"10.2168\/lmcs-9(4:15)2013","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T09:37:51Z","timestamp":1405417071000},"source":"Crossref","is-referenced-by-count":0,"title":["Approximation systems for functions in topological and in metric spaces"],"prefix":"10.46298","volume":"Volume 9, Issue 4","author":[{"given":"Dimiter","family":"Skordev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,11,20]]},"reference":[{"key":"847:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/890\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/890\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:58:44Z","timestamp":1681243124000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/890"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,20]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(4:15)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1310.5656","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1310.5656","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2013,11,20]]},"article-number":"890"}}