{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T17:27:23Z","timestamp":1648747643651},"reference-count":26,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,1,1]]},"abstract":"<jats:title>Functional Space <jats:italic>C<\/jats:italic>(\u03c9), <jats:italic>C<\/jats:italic><jats:sub>0<\/jats:sub>(\u03c9)<\/jats:title>\n        <jats:p>In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.<\/jats:p>","DOI":"10.2478\/v10037-012-0003-3","type":"journal-article","created":{"date-parts":[[2012,9,13]],"date-time":"2012-09-13T01:22:44Z","timestamp":1347499364000},"page":"15-22","source":"Crossref","is-referenced-by-count":0,"title":["Functional Space C(\u03c9), C0(\u03c9)"],"prefix":"10.2478","volume":"20","author":[{"given":"Katuhiko","family":"Kanazashi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroyuki","family":"Okazaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"issue":"1","key":"1","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"2","first-page":"175","article-title":"Binary operations","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"3","key":"3","first-page":"507","article-title":"The complex numbers","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"4","first-page":"153","article-title":"Functions from a set to a set","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"5","first-page":"357","article-title":"Partial functions","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"6","first-page":"47","article-title":"Some basic properties of sets","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"7","first-page":"383","article-title":"Compact spaces","volume":"1","author":"Agata Darmochwa\u0142","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"3","key":"8","first-page":"237","article-title":"Banach algebra of bounded complex linear operators","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"2","key":"9","first-page":"191","article-title":"Banach space of absolute summable complex sequences","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"2","key":"10","first-page":"201","article-title":"Complex Banach space of bounded linear operators","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"2","key":"11","first-page":"93","article-title":"Complex linear space and complex normed space","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"2","key":"12","first-page":"109","article-title":"Complex linear space of complex sequences","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"3","key":"13","first-page":"231","article-title":"Complex valued functions space","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"3","key":"14","first-page":"403","article-title":"Continuous functions on real and complex normed linear spaces","volume":"12","author":"Noboru Endou","year":"2004","journal-title":"Formalized Mathematics"},{"issue":"1","key":"15","first-page":"35","article-title":"Basic properties of real numbers","volume":"1","author":"Krzysztof Hryniewiecki","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"121","DOI":"10.2478\/v10037-011-0019-0","article-title":"Banach algebra of bounded complex-valued functionals","volume":"19","author":"Katuhiko Kanazashi","year":"2011","journal-title":"Formalized Mathematics"},{"issue":"2","key":"17","first-page":"335","article-title":"Abelian groups, fields and vector spaces","volume":"1","author":"Eugeniusz Kusak","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"18","doi-asserted-by":"publisher","first-page":"67","DOI":"10.2478\/v10037-009-0007-9","article-title":"Complex function differentiability","volume":"17","author":"Chanapat Pacharapokin","year":"2009","journal-title":"Formalized Mathematics"},{"issue":"1","key":"19","first-page":"223","article-title":"Topological spaces and continuous functions","volume":"1","author":"Beata Padlewska","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"20","doi-asserted-by":"publisher","first-page":"115","DOI":"10.2478\/v10037-008-0017-z","article-title":"Banach algebra of bounded functionals","volume":"16","author":"Yasunari Shidama","year":"2008","journal-title":"Formalized Mathematics"},{"issue":"2","key":"21","first-page":"329","article-title":"Binary operations applied to functions","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"5","key":"22","first-page":"821","article-title":"Groups","volume":"1","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"2","key":"23","first-page":"291","article-title":"Vectors in real linear space","volume":"1","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"24","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"25","first-page":"73","article-title":"Relations and their basic properties","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"},{"issue":"1","key":"26","first-page":"181","article-title":"Relations defined on sets","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/20\/1\/article-p15.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2012.20.issue-1\/v10037-012-0003-3\/v10037-012-0003-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:28:28Z","timestamp":1590852508000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-012-0003-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,1]]},"references-count":26,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/v10037-012-0003-3","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2012,1,1]]}}}