{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T18:29:23Z","timestamp":1649010563511},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2016,9,1]],"date-time":"2016-09-01T00:00:00Z","timestamp":1472688000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> In this article, we formalize in Mizar [1] the notion of uniform space introduced by Andr\u00e9 Weil using the concepts of entourages [2].<\/jats:p>\n               <jats:p>We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group.<\/jats:p>\n               <jats:p>Next, we define the concept of the partition topology. Following the Vlach\u2019s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation.<\/jats:p>\n               <jats:p>Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\\A) \u00d7 (X\\A)) \u222a (A\u00d7A) is presented.<\/jats:p>","DOI":"10.1515\/forma-2016-0018","type":"journal-article","created":{"date-parts":[[2017,2,14]],"date-time":"2017-02-14T10:02:03Z","timestamp":1487066523000},"page":"215-226","source":"Crossref","is-referenced-by-count":1,"title":["Uniform Space"],"prefix":"10.1515","volume":"24","author":[{"given":"Roland","family":"Coghetto","sequence":"first","affiliation":[{"name":"Rue de la Brasserie 5 7100 La Louvi\u00e8re, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,2,21]]},"reference":[{"key":"2021040611133400103_j_forma-2016-0018_ref_1_w2aab2b8b4b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Grzegorz Bancerek, Czes\u0142aw Bylinski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007\/978-3-319-20615-8_17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2021040611133400103_j_forma-2016-0018_ref_2_w2aab2b8b4b1b7b1ab1ab2Aa","unstructured":"[2] Nicolas Bourbaki. General Topology: Chapters 1-4. Springer Science and Business Media, 2013."},{"key":"2021040611133400103_j_forma-2016-0018_ref_3_w2aab2b8b4b1b7b1ab1ab3Aa","unstructured":"[3] Czes\u0142aw Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990."},{"key":"2021040611133400103_j_forma-2016-0018_ref_4_w2aab2b8b4b1b7b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"[4] Mai Gehrke, Serge Grigorieff, and Jean-\u00c9ric Pin. A topological approach to recognition. In Automata, Languages and Programming, pages 151-162. Springer, 2010.","DOI":"10.1007\/978-3-642-14162-1_13"},{"key":"2021040611133400103_j_forma-2016-0018_ref_5_w2aab2b8b4b1b7b1ab1ab5Aa","unstructured":"[5] Stanis\u0142awa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990."},{"key":"2021040611133400103_j_forma-2016-0018_ref_6_w2aab2b8b4b1b7b1ab1ab6Aa","unstructured":"[6] Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991."},{"key":"2021040611133400103_j_forma-2016-0018_ref_7_w2aab2b8b4b1b7b1ab1ab7Aa","unstructured":"[7] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990."},{"key":"2021040611133400103_j_forma-2016-0018_ref_8_w2aab2b8b4b1b7b1ab1ab8Aa","unstructured":"[8] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990."},{"key":"2021040611133400103_j_forma-2016-0018_ref_9_w2aab2b8b4b1b7b1ab1ab9Aa","unstructured":"[9] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990."},{"key":"2021040611133400103_j_forma-2016-0018_ref_10_w2aab2b8b4b1b7b1ab1ac10Aa","unstructured":"[10] Milan Vlach. Algebraic and topological aspects of rough set theory. In Fourth International Workshop on Computational Intelligence & Applications, IEEE SMC Hiroshima Chapter, Hiroshima University, Japan, December 10&11, 2008."},{"key":"2021040611133400103_j_forma-2016-0018_ref_11_w2aab2b8b4b1b7b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"[11] Milan Vlach. Topologies of approximation spaces of rough set theory. In Interval\/ Probabilistic Uncertainty and Non-Classical Logics, pages 176-186. Springer, 2008.","DOI":"10.1007\/978-3-540-77664-2_14"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/24\/3\/article-p215.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T16:04:46Z","timestamp":1617725086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,1]]},"references-count":11,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,2,21]]},"published-print":{"date-parts":[[2016,9,1]]}},"alternative-id":["10.1515\/forma-2016-0018"],"URL":"https:\/\/doi.org\/10.1515\/forma-2016-0018","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,1]]}}}