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http://hdl.handle.net/11320/12390Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Yamazaki, Hiroshi | - |
| dc.contributor.author | Miyajima, Keiichi | - |
| dc.contributor.author | Shidama, Yasunari | - |
| dc.date.accessioned | 2022-01-04T06:48:52Z | - |
| dc.date.available | 2022-01-04T06:48:52Z | - |
| dc.date.issued | 2021 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 29, Issue 2, Pages 87-94 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/12390 | - |
| dc.description.abstract | In this article we formalize the Ascoli-Arzelà theorem [5], [6], [8] in Mizar [1], [2]. First, we gave definitions of equicontinuousness and equiboundedness of a set of continuous functions [12], [7], [3], [9]. Next, we formalized the Ascoli-Arzelà theorem using those definitions, and proved this theorem. | pl |
| dc.description.sponsorship | This work was supported by JSPS KAKENHI Grant Numbers JP17K00182. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | - |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | - |
| dc.subject | Ascoli-Arzela’s theorem | pl |
| dc.subject | equicontinuousness of continuous functions | pl |
| dc.subject | equiboundedness of continuous functions | pl |
| dc.title | Ascoli-Arzelà Theorem | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2021 University of Białymstoku | pl |
| dc.rights.holder | CC-BY-SA License ver. 3.0 or later | pl |
| dc.identifier.doi | 10.2478/forma-2021-0009 | - |
| dc.description.Affiliation | Hiroshi Yamazaki - Nagano Prefectural Institute of Technology, Nagano, Japan | pl |
| dc.description.Affiliation | Keiichi Miyajima - Ibaraki University Faculty of Engineering, Hitachi, Ibaraki, Japan | pl |
| dc.description.Affiliation | Yasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japan | pl |
| dc.description.references | Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, 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. | pl |
| dc.description.references | Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6. | pl |
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| dc.description.references | Noboru Endou, Yasunari Shidama, and Katsumasa Okamura. Baire’s category theorem and some spaces generated from real normed space. Formalized Mathematics, 14(4): 213–219, 2006. doi:10.2478/v10037-006-0024-x. | pl |
| dc.description.references | Serge Lang. Real and Functional Analysis (Texts in Mathematics). Springer-Verlag, 1993. | pl |
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| dc.description.references | Tohru Ozawa. Ascoli-Arzelà theorem. 2012. | pl |
| dc.description.references | Michael Read and Barry Simon. Functional Analysis (Methods of Modern Mathematical Physics). Academic Press, 1980. | pl |
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| dc.description.references | Yasumasa Suzuki, Noboru Endou, and Yasunari Shidama. Banach space of absolute summable real sequences. Formalized Mathematics, 11(4):377–380, 2003. | pl |
| dc.description.references | Hiroshi Yamazaki, Keiichi Miyajima, and Yasunari Shidama. Functional space consisted by continuous functions on topological space. Formalized Mathematics, 29(1):49–62, 2021. doi:10.2478/forma-2021-0005. | pl |
| dc.description.references | Kôsaku Yosida. Functional Analysis. Springer, 1980. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 29 | pl |
| dc.description.issue | 2 | pl |
| dc.description.firstpage | 87 | pl |
| dc.description.lastpage | 94 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2021, Volume 29, Issue 2 | |
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|---|---|---|---|---|
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