{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T23:01:09Z","timestamp":1648854069194},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,1,1]]},"DOI":"10.2478\/v10037-009-0001-2","type":"journal-article","created":{"date-parts":[[2009,3,21]],"date-time":"2009-03-21T01:07:25Z","timestamp":1237597645000},"page":"1-9","source":"Crossref","is-referenced-by-count":3,"title":["The Real Vector Spaces of Finite Sequences are Finite Dimensional"],"prefix":"10.2478","volume":"17","author":[{"given":"Yatsuka","family":"Nakamura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Artur","family":"Korni\u0142owicz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nagato","family":"Oya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"1","first-page":"179","article-title":"The inner product of finite sequences and of points of n-dimensional topological space","volume":"2","author":"Yatsuka Kanchun","year":"2003","journal-title":"Formalized Mathematics"},{"key":"2","first-page":"377","article-title":"Cardinal numbers","volume":"2","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"3","first-page":"41","article-title":"The fundamental properties of natural numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"4","first-page":"107","article-title":"Segments of natural numbers and finite sequences","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"5","first-page":"245","article-title":"Basic functions and operations on functions","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"6","first-page":"529","article-title":"Finite sequences and tuples of elements of a non-empty sets","volume":"3","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"7","first-page":"55","article-title":"Functions and their basic properties","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"8","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"},{"key":"9","first-page":"357","article-title":"Partial functions","volume":"2","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"10","first-page":"47","article-title":"Some basic properties of sets","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"11","first-page":"661","article-title":"The sum and product of finite sequences of real numbers","volume":"4","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"12","first-page":"411","article-title":"The Steinitz theorem and the dimension of a real linear space","volume":"3","author":"Jing-Chao Chen","year":"1997","journal-title":"Formalized Mathematics"},{"key":"13","first-page":"165","article-title":"Finite sets","volume":"1","author":"Agata Darmochwa\u0142","year":"1990","journal-title":"Formalized Mathematics"},{"key":"14","first-page":"599","article-title":"The Euclidean space","volume":"4","author":"Agata Darmochwa\u0142","year":"1991","journal-title":"Formalized Mathematics"},{"key":"15","first-page":"23","article-title":"Dimension of real unitary space","volume":"1","author":"Noboru Endou","year":"2003","journal-title":"Formalized Mathematics"},{"key":"16","first-page":"17","article-title":"Linear combinations in real unitary space","volume":"1","author":"Noboru Endou","year":"2003","journal-title":"Formalized Mathematics"},{"key":"17","first-page":"577","article-title":"Completeness of the real Euclidean space","volume":"4","author":"Noboru Endou","year":"2005","journal-title":"Formalized Mathematics"},{"key":"18","first-page":"269","article-title":"Real sequences and basic operations on them","volume":"2","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"19","first-page":"1","article-title":"Sorting operators for finite sequences","volume":"1","author":"Yatsuka Nakamura","year":"2004","journal-title":"Formalized Mathematics"},{"key":"20","first-page":"555","article-title":"Real functions spaces","volume":"3","author":"Henryk Oryszczyszyn","year":"1990","journal-title":"Formalized Mathematics"},{"key":"21","first-page":"147","article-title":"Families of sets","volume":"1","author":"Beata Padlewska","year":"1990","journal-title":"Formalized Mathematics"},{"key":"22","first-page":"223","article-title":"Topological spaces and continuous functions","volume":"1","author":"Beata Padlewska","year":"1990","journal-title":"Formalized Mathematics"},{"key":"23","doi-asserted-by":"publisher","first-page":"127","DOI":"10.2478\/v10037-007-00014-7","article-title":"Determinant and inverse of matrices of real elements","volume":"3","author":"Nobuyuki Tamura","year":"2007","journal-title":"Formalized Mathematics"},{"key":"24","first-page":"329","article-title":"Binary operations applied to functions","volume":"2","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"25","first-page":"115","article-title":"Domains and their Cartesian products","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"26","first-page":"847","article-title":"Basis of real linear space","volume":"5","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"27","first-page":"979","article-title":"Binary operations on finite sequences","volume":"5","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"28","first-page":"581","article-title":"Linear combinations in real linear space","volume":"3","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"29","first-page":"297","article-title":"Subspaces and cosets of subspaces in real linear space","volume":"2","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"30","first-page":"291","article-title":"Vectors in real linear space","volume":"2","author":"Wojciech Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"31","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"32","first-page":"73","article-title":"Relations and their basic properties","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"33","first-page":"181","article-title":"Relations defined on sets","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"34","first-page":"471","article-title":"On replace function and swap function for finite sequences","volume":"3","author":"Hiroshi Yamazaki","year":"2001","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2009.17.issue-1\/v10037-009-0001-2\/v10037-009-0001-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:37Z","timestamp":1590852457000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-009-0001-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,1]]},"references-count":34,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/v10037-009-0001-2","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2009,1,1]]}}}